תרגול משפט הקוסינוסים - שלב 1 – חלק ב׳

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 8^2 - 2 \cdot 8 \cdot 8 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 64 + 64 - 2 \cdot 8 \cdot 8 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 17.15\)

\(c = \sqrt{17.15} = 4.14\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 5^2 + 9^2 - 2 \cdot 5 \cdot 9 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 25 + 81 - 2 \cdot 5 \cdot 9 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 42.36\)

\(c = \sqrt{42.36} = 6.51\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 4^2 + 6^2 - 2 \cdot 4 \cdot 6 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 16 + 36 - 2 \cdot 4 \cdot 6 \cdot \frac{1}{2}\)

\(c^2 = 28\)

\(c = \sqrt{28} = 5.29\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 10^2 + 4^2 - 2 \cdot 10 \cdot 4 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 100 + 16 - 2 \cdot 10 \cdot 4 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 59.43\)

\(c = \sqrt{59.43} = 7.71\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 5^2 + 11^2 - 2 \cdot 5 \cdot 11 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 25 + 121 - 2 \cdot 5 \cdot 11 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 50.74\)

\(c = \sqrt{50.74} = 7.12\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 8^2 - 2 \cdot 8 \cdot 8 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 64 + 64 - 2 \cdot 8 \cdot 8 \cdot \frac{1}{2}\)

\(c^2 = 64\)

\(c = \sqrt{64} = 8\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 7^2 - 2 \cdot 8 \cdot 7 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 64 + 49 - 2 \cdot 8 \cdot 7 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 16.01\)

\(c = \sqrt{16.01} = 4\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 6^2 + 5^2 - 2 \cdot 6 \cdot 5 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 36 + 25 - 2 \cdot 6 \cdot 5 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 18.57\)

\(c = \sqrt{18.57} = 4.31\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 6^2 + 11^2 - 2 \cdot 6 \cdot 11 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 36 + 121 - 2 \cdot 6 \cdot 11 \cdot \frac{1}{2}\)

\(c^2 = 91\)

\(c = \sqrt{91} = 9.54\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 7^2 + 10^2 - 2 \cdot 7 \cdot 10 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 49 + 100 - 2 \cdot 7 \cdot 10 \cdot \frac{1}{2}\)

\(c^2 = 79\)

\(c = \sqrt{79} = 8.89\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 5^2 + 9^2 - 2 \cdot 5 \cdot 9 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 25 + 81 - 2 \cdot 5 \cdot 9 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 28.06\)

\(c = \sqrt{28.06} = 5.3\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 7^2 + 7^2 - 2 \cdot 7 \cdot 7 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 49 + 49 - 2 \cdot 7 \cdot 7 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 13.13\)

\(c = \sqrt{13.13} = 3.62\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 4^2 + 8^2 - 2 \cdot 4 \cdot 8 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 16 + 64 - 2 \cdot 4 \cdot 8 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 34.75\)

\(c = \sqrt{34.75} = 5.89\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 5^2 - 2 \cdot 11 \cdot 5 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 121 + 25 - 2 \cdot 11 \cdot 5 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 50.74\)

\(c = \sqrt{50.74} = 7.12\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 9^2 - 2 \cdot 11 \cdot 9 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 121 + 81 - 2 \cdot 11 \cdot 9 \cdot \frac{1}{2}\)

\(c^2 = 103\)

\(c = \sqrt{103} = 10.15\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 4^2 + 10^2 - 2 \cdot 4 \cdot 10 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 16 + 100 - 2 \cdot 4 \cdot 10 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 46.72\)

\(c = \sqrt{46.72} = 6.84\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 9^2 + 5^2 - 2 \cdot 9 \cdot 5 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 81 + 25 - 2 \cdot 9 \cdot 5 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 42.36\)

\(c = \sqrt{42.36} = 6.51\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 6^2 + 6^2 - 2 \cdot 6 \cdot 6 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 36 + 36 - 2 \cdot 6 \cdot 6 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 21.09\)

\(c = \sqrt{21.09} = 4.59\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 10^2 - 2 \cdot 8 \cdot 10 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 64 + 100 - 2 \cdot 8 \cdot 10 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 50.86\)

\(c = \sqrt{50.86} = 7.13\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 7^2 + 11^2 - 2 \cdot 7 \cdot 11 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 49 + 121 - 2 \cdot 7 \cdot 11 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 61.11\)

\(c = \sqrt{61.11} = 7.82\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 4^2 + 5^2 - 2 \cdot 4 \cdot 5 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 16 + 25 - 2 \cdot 4 \cdot 5 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 6.36\)

\(c = \sqrt{6.36} = 2.52\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 4^2 - 2 \cdot 11 \cdot 4 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 121 + 16 - 2 \cdot 11 \cdot 4 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 74.77\)

\(c = \sqrt{74.77} = 8.65\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 6^2 - 2 \cdot 11 \cdot 6 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 121 + 36 - 2 \cdot 11 \cdot 6 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 42.68\)

\(c = \sqrt{42.68} = 6.53\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 9^2 + 6^2 - 2 \cdot 9 \cdot 6 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 81 + 36 - 2 \cdot 9 \cdot 6 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 40.63\)

\(c = \sqrt{40.63} = 6.37\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 11^2 - 2 \cdot 11 \cdot 11 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 121 + 121 - 2 \cdot 11 \cdot 11 \cdot \frac{1}{2}\)

\(c^2 = 121\)

\(c = \sqrt{121} = 11\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 5^2 + 7^2 - 2 \cdot 5 \cdot 7 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 25 + 49 - 2 \cdot 5 \cdot 7 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 24.5\)

\(c = \sqrt{24.5} = 4.95\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 10^2 + 4^2 - 2 \cdot 10 \cdot 4 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 100 + 16 - 2 \cdot 10 \cdot 4 \cdot \frac{1}{2}\)

\(c^2 = 76\)

\(c = \sqrt{76} = 8.72\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 10^2 + 9^2 - 2 \cdot 10 \cdot 9 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 100 + 81 - 2 \cdot 10 \cdot 9 \cdot \frac{1}{2}\)

\(c^2 = 91\)

\(c = \sqrt{91} = 9.54\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 5^2 + 6^2 - 2 \cdot 5 \cdot 6 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 25 + 36 - 2 \cdot 5 \cdot 6 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 18.57\)

\(c = \sqrt{18.57} = 4.31\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 10^2 - 2 \cdot 11 \cdot 10 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 121 + 100 - 2 \cdot 11 \cdot 10 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 65.44\)

\(c = \sqrt{65.44} = 8.09\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 8^2 - 2 \cdot 11 \cdot 8 \cdot \cos(30°)\)

\(\cos(30°) = \frac{\sqrt{3}}{2}\)

\(c^2 = 121 + 64 - 2 \cdot 11 \cdot 8 \cdot \frac{\sqrt{3}}{2}\)

\(c^2 = 32.58\)

\(c = \sqrt{32.58} = 5.71\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 10^2 + 9^2 - 2 \cdot 10 \cdot 9 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 100 + 81 - 2 \cdot 10 \cdot 9 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 53.72\)

\(c = \sqrt{53.72} = 7.33\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 5^2 + 8^2 - 2 \cdot 5 \cdot 8 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 25 + 64 - 2 \cdot 5 \cdot 8 \cdot \frac{1}{2}\)

\(c^2 = 49\)

\(c = \sqrt{49} = 7\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 11^2 - 2 \cdot 8 \cdot 11 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 64 + 121 - 2 \cdot 8 \cdot 11 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 60.55\)

\(c = \sqrt{60.55} = 7.78\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 11^2 + 5^2 - 2 \cdot 11 \cdot 5 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 121 + 25 - 2 \cdot 11 \cdot 5 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 68.22\)

\(c = \sqrt{68.22} = 8.26\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 7^2 + 7^2 - 2 \cdot 7 \cdot 7 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 49 + 49 - 2 \cdot 7 \cdot 7 \cdot \frac{1}{2}\)

\(c^2 = 49\)

\(c = \sqrt{49} = 7\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 11^2 - 2 \cdot 8 \cdot 11 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 64 + 121 - 2 \cdot 8 \cdot 11 \cdot \frac{1}{2}\)

\(c^2 = 97\)

\(c = \sqrt{97} = 9.85\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 10^2 + 7^2 - 2 \cdot 10 \cdot 7 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 100 + 49 - 2 \cdot 10 \cdot 7 \cdot \frac{1}{2}\)

\(c^2 = 79\)

\(c = \sqrt{79} = 8.89\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 8^2 + 9^2 - 2 \cdot 8 \cdot 9 \cdot \cos(45°)\)

\(\cos(45°) = \frac{\sqrt{2}}{2}\)

\(c^2 = 64 + 81 - 2 \cdot 8 \cdot 9 \cdot \frac{\sqrt{2}}{2}\)

\(c^2 = 43.18\)

\(c = \sqrt{43.18} = 6.57\)

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

\(c^2 = 10^2 + 5^2 - 2 \cdot 10 \cdot 5 \cdot \cos(60°)\)

\(\cos(60°) = \frac{1}{2}\)

\(c^2 = 100 + 25 - 2 \cdot 10 \cdot 5 \cdot \frac{1}{2}\)

\(c^2 = 75\)

\(c = \sqrt{75} = 8.66\)