Sine Rule — Step 1 — Dynamic Practice

Sine Rule — Step 1 — Dynamic Practice. Practice questions to deepen understanding of using the sine rule to find a missing side in a triangle. Online math practice with full solutions and step-by-step explanations.

Dynamic practice in the sine rule (step 1) — using a/sin A = b/sin B to find a missing side. New questions every attempt.

40 questions

Question 1
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 45°
• side a (opposite angle A) = 25

ABC30°45°?a=25b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°45°?a=25b=35.36c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{25}{\sin(30°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{25 \cdot \sin(45°)}{\sin(30°)} = \frac{25 \cdot \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 35.36\)
Answer: b = 35.36
Question 2
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 9

ABC30°60°?a=9b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=9b=15.59c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{9}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{9 \cdot \sin(60°)}{\sin(30°)} = \frac{9 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 15.59\)
Answer: b = 15.59
Question 3
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 5

ABC45°60°?a=5b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=5b=6.12c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{5}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{5 \cdot \sin(60°)}{\sin(45°)} = \frac{5 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 6.12\)
Answer: b = 6.12
Question 4
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 9

ABC45°60°?a=9b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=9b=11.02c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{9}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{9 \cdot \sin(60°)}{\sin(45°)} = \frac{9 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 11.02\)
Answer: b = 11.02
Question 5
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 16

ABC45°60°?a=16b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=16b=19.6c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{16}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{16 \cdot \sin(60°)}{\sin(45°)} = \frac{16 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 19.6\)
Answer: b = 19.6
Question 6
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 29

ABC45°30°?a=29b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=29b=20.51c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{29}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{29 \cdot \sin(30°)}{\sin(45°)} = \frac{29 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 20.51\)
Answer: b = 20.51
Question 7
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 45°
• side a (opposite angle A) = 12

ABC30°45°?a=12b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°45°?a=12b=16.97c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{12}{\sin(30°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{12 \cdot \sin(45°)}{\sin(30°)} = \frac{12 \cdot \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 16.97\)
Answer: b = 16.97
Question 8
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 45°
• side a (opposite angle A) = 29

ABC60°45°?a=29b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°45°?a=29b=23.68c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{29}{\sin(60°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{29 \cdot \sin(45°)}{\sin(60°)} = \frac{29 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = 23.68\)
Answer: b = 23.68
Question 9
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 15

ABC30°60°?a=15b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=15b=25.98c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{15}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{15 \cdot \sin(60°)}{\sin(30°)} = \frac{15 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 25.98\)
Answer: b = 25.98
Question 10
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 28

ABC30°60°?a=28b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=28b=48.5c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{28}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{28 \cdot \sin(60°)}{\sin(30°)} = \frac{28 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 48.5\)
Answer: b = 48.5
Question 11
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 24

ABC45°60°?a=24b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=24b=29.39c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{24}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{24 \cdot \sin(60°)}{\sin(45°)} = \frac{24 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 29.39\)
Answer: b = 29.39
Question 12
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 13

ABC45°30°?a=13b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=13b=9.19c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{13}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{13 \cdot \sin(30°)}{\sin(45°)} = \frac{13 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 9.19\)
Answer: b = 9.19
Question 13
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 45°
• side a (opposite angle A) = 11

ABC30°45°?a=11b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°45°?a=11b=15.56c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{11}{\sin(30°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{11 \cdot \sin(45°)}{\sin(30°)} = \frac{11 \cdot \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 15.56\)
Answer: b = 15.56
Question 14
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 24

ABC30°60°?a=24b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=24b=41.57c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{24}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{24 \cdot \sin(60°)}{\sin(30°)} = \frac{24 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 41.57\)
Answer: b = 41.57
Question 15
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 12

ABC30°60°?a=12b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=12b=20.78c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{12}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{12 \cdot \sin(60°)}{\sin(30°)} = \frac{12 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 20.78\)
Answer: b = 20.78
Question 16
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 18

ABC45°30°?a=18b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=18b=12.73c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{18}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{18 \cdot \sin(30°)}{\sin(45°)} = \frac{18 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 12.73\)
Answer: b = 12.73
Question 17
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 45°
• side a (opposite angle A) = 27

ABC60°45°?a=27b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°45°?a=27b=22.05c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{27}{\sin(60°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{27 \cdot \sin(45°)}{\sin(60°)} = \frac{27 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = 22.05\)
Answer: b = 22.05
Question 18
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 19

ABC30°60°?a=19b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=19b=32.91c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{19}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{19 \cdot \sin(60°)}{\sin(30°)} = \frac{19 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 32.91\)
Answer: b = 32.91
Question 19
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 45°
• side a (opposite angle A) = 11

ABC60°45°?a=11b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°45°?a=11b=8.98c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{11}{\sin(60°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{11 \cdot \sin(45°)}{\sin(60°)} = \frac{11 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = 8.98\)
Answer: b = 8.98
Question 20
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 11

ABC30°60°?a=11b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=11b=19.05c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{11}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{11 \cdot \sin(60°)}{\sin(30°)} = \frac{11 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 19.05\)
Answer: b = 19.05
Question 21
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 10

ABC30°60°?a=10b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=10b=17.32c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{10}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{10 \cdot \sin(60°)}{\sin(30°)} = \frac{10 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 17.32\)
Answer: b = 17.32
Question 22
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 7

ABC45°30°?a=7b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=7b=4.95c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{7}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{7 \cdot \sin(30°)}{\sin(45°)} = \frac{7 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 4.95\)
Answer: b = 4.95
Question 23
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 30°
• side a (opposite angle A) = 14

ABC60°30°?a=14b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°30°?a=14b=8.08c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{14}{\sin(60°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{14 \cdot \sin(30°)}{\sin(60°)} = \frac{14 \cdot \frac{1}{2}}{\frac{\sqrt{3}}{2}} = 8.08\)
Answer: b = 8.08
Question 24
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 10

ABC45°60°?a=10b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=10b=12.25c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{10}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{10 \cdot \sin(60°)}{\sin(45°)} = \frac{10 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 12.25\)
Answer: b = 12.25
Question 25
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 17

ABC30°60°?a=17b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=17b=29.44c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{17}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{17 \cdot \sin(60°)}{\sin(30°)} = \frac{17 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 29.44\)
Answer: b = 29.44
Question 26
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 25

ABC45°60°?a=25b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=25b=30.62c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{25}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{25 \cdot \sin(60°)}{\sin(45°)} = \frac{25 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 30.62\)
Answer: b = 30.62
Question 27
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 45°
• side a (opposite angle A) = 10

ABC60°45°?a=10b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°45°?a=10b=8.16c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{10}{\sin(60°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{10 \cdot \sin(45°)}{\sin(60°)} = \frac{10 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = 8.16\)
Answer: b = 8.16
Question 28
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 45°
• side a (opposite angle A) = 26

ABC30°45°?a=26b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°45°?a=26b=36.77c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{26}{\sin(30°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{26 \cdot \sin(45°)}{\sin(30°)} = \frac{26 \cdot \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 36.77\)
Answer: b = 36.77
Question 29
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 22

ABC30°60°?a=22b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=22b=38.11c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{22}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{22 \cdot \sin(60°)}{\sin(30°)} = \frac{22 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 38.11\)
Answer: b = 38.11
Question 30
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 22

ABC45°30°?a=22b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=22b=15.56c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{22}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{22 \cdot \sin(30°)}{\sin(45°)} = \frac{22 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 15.56\)
Answer: b = 15.56
Question 31
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 45°
• side a (opposite angle A) = 18

ABC30°45°?a=18b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°45°?a=18b=25.46c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{18}{\sin(30°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{18 \cdot \sin(45°)}{\sin(30°)} = \frac{18 \cdot \frac{\sqrt{2}}{2}}{\frac{1}{2}} = 25.46\)
Answer: b = 25.46
Question 32
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 12

ABC45°60°?a=12b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=12b=14.7c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{12}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{12 \cdot \sin(60°)}{\sin(45°)} = \frac{12 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 14.7\)
Answer: b = 14.7
Question 33
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 8

ABC45°60°?a=8b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=8b=9.8c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{8}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{8 \cdot \sin(60°)}{\sin(45°)} = \frac{8 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 9.8\)
Answer: b = 9.8
Question 34
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 30°
• Angle B = 60°
• side a (opposite angle A) = 29

ABC30°60°?a=29b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC30°60°?a=29b=50.23c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{29}{\sin(30°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{29 \cdot \sin(60°)}{\sin(30°)} = \frac{29 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{2}} = 50.23\)
Answer: b = 50.23
Question 35
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 21

ABC45°30°?a=21b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=21b=14.85c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{21}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{21 \cdot \sin(30°)}{\sin(45°)} = \frac{21 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 14.85\)
Answer: b = 14.85
Question 36
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 45°
• side a (opposite angle A) = 18

ABC60°45°?a=18b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°45°?a=18b=14.7c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{18}{\sin(60°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{18 \cdot \sin(45°)}{\sin(60°)} = \frac{18 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = 14.7\)
Answer: b = 14.7
Question 37
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 24

ABC45°30°?a=24b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=24b=16.97c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{24}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{24 \cdot \sin(30°)}{\sin(45°)} = \frac{24 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 16.97\)
Answer: b = 16.97
Question 38
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 60°
• Angle B = 45°
• side a (opposite angle A) = 15

ABC60°45°?a=15b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC60°45°?a=15b=12.25c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{15}{\sin(60°)} = \frac{b}{\sin(45°)}\)

🔢 Step 2: Solve
\(b = \frac{15 \cdot \sin(45°)}{\sin(60°)} = \frac{15 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = 12.25\)
Answer: b = 12.25
Question 39
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 30°
• side a (opposite angle A) = 23

ABC45°30°?a=23b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°30°?a=23b=16.26c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{23}{\sin(45°)} = \frac{b}{\sin(30°)}\)

🔢 Step 2: Solve
\(b = \frac{23 \cdot \sin(30°)}{\sin(45°)} = \frac{23 \cdot \frac{1}{2}}{\frac{\sqrt{2}}{2}} = 16.26\)
Answer: b = 16.26
Question 40
2.50 pts
📐 Law of Sines in triangle ABC:

In triangle ABC the following are given:
• Angle A = 45°
• Angle B = 60°
• side a (opposite angle A) = 20

ABC45°60°?a=20b=?c=?
Find side b (opposite angle B).
Explanation:
Solution - Law of Sines in triangle ABC:

ABC45°60°?a=20b=24.49c=?
📝 Law of Sines:
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)
🔢 Step 1: Substitute the data
\(\frac{20}{\sin(45°)} = \frac{b}{\sin(60°)}\)

🔢 Step 2: Solve
\(b = \frac{20 \cdot \sin(60°)}{\sin(45°)} = \frac{20 \cdot \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = 24.49\)
Answer: b = 24.49