The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
-$$a = 8 , b = 11 , C = 123 ^ { \circ }$$
A) $\mathrm { c } = 16.8 , \mathrm {~A} = 24 ^ { \circ } , \mathrm { B } = 33 ^ { \circ }$
B) $\mathrm { c } = 19.7 , \mathrm {~A} = 26 ^ { \circ } , \mathrm { B } = 31 ^ { \circ }$
C) $\mathrm { c } = 22.6 , \mathrm {~A} = 22 ^ { \circ } , \mathrm { B } = 35 ^ { \circ }$
D) no triangle

Question

Quizplus · Accepted Answer

The Law of Cosines states that in a triangle with sides a, b, and c, and angles A, B, and C opposite those sides, respectively,$$c^2 = a^2 + b^2 - 2ab \cos{C}$$Using this formula, we can solve for c:$$c = \sqrt{a^2 + b^2 - 2ab \cos{C}}$$$$c = \sqrt{8^2 + 11^2 - 2(8)(11) \cos{123^\circ}}$$$$c \approx 16.8$$We can also use the Law of Cosines to solve for the other angles:$$\cos{A} = \frac{b^2 + c^2 - a^2}{2bc}$$$$\cos{A} = \frac{11^2 + 16.8^2 - 8^2}{2(11)(16.8)}$$$$\cos{A} \approx 0.9135$$$$A \approx 24^\circ$$$$\cos{B} = \frac{a^2 + c^2 - b^2}{2ac}$$$$\cos{B} = \frac{8^2 + 16.8^2 - 11^2}{2(8)(16.8)}$$$$\cos{B} \approx 0.8387$$$$B \approx 33^\circ$$Therefore, the correct answer is A) $c = 16.8, A = 24^\circ, B = 33^\circ$.

The Law of Cosines 1 Use the Law of Cosines a=8,b=11,C=123∘a = 8 , b = 11 , C = 123 ^ { \circ }a=8,b=11,C=123∘

The Law of Cosines
1 Use the Law of Cosines $a = 8 , b = 11 , C = 123 ^ { \circ }$