The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
-$$b = 6 , c = 10 , A = 119 ^ { \circ }$$
A) $a = 13.9 , B = 22 ^ { \circ } , C = 39 ^ { \circ }$
B) $\mathrm { a } = 16.8 , \mathrm {~B} = 24 ^ { \circ } , \mathrm { C } = 37 ^ { \circ }$
C) $\mathrm { a } = 19.7 , \mathrm {~B} = 20 ^ { \circ } , \mathrm { C } = 41 ^ { \circ }$
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, the following equation holds:$$a^2 = b^2 + c^2 - 2bc \cos A$$Using this equation, we can solve for the unknown side a:$$a^2 = 6^2 + 10^2 - 2(6)(10) \cos 119 ^ { \circ }$$$$a^2 = 36 + 100 - 120 \cos 119 ^ { \circ }$$$$a^2 = 136 - 120 \cos 119 ^ { \circ }$$$$a = \sqrt { 136 - 120 \cos 119 ^ { \circ } }$$$$a \approx 13.9$$We can also use the Law of Cosines to solve for the unknown angles B and C:$$B = \cos ^ { - 1 } \frac { a ^ { 2 } + c ^ { 2 } - b ^ { 2 } } { 2 a c }$$$$B = \cos ^ { - 1 } \frac { 13.9 ^ { 2 } + 10 ^ { 2 } - 6 ^ { 2 } } { 2 ( 13.9 ) ( 10 ) }$$$$B \approx 22 ^ { \circ }$$$$C = 180 ^ { \circ } - A - B$$$$C = 180 ^ { \circ } - 119 ^ { \circ } - 22 ^ { \circ }$$$$C \approx 39 ^ { \circ }$$Therefore, the correct answer is A) $a = 13.9 , B = 22 ^ { \circ } , C = 39 ^ { \circ }$.

The Law of Cosines 1 Use the Law of Cosines b=6,c=10,A=119∘b = 6 , c = 10 , A = 119 ^ { \circ }b=6,c=10,A=119∘

The Law of Cosines
1 Use the Law of Cosines $b = 6 , c = 10 , A = 119 ^ { \circ }$