Given $a = 9 , b = 12 , \text { and } c = 7 ,$ , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.
A)$96.38 ^ { \circ }$
B) $48.19 ^ { \circ }$
C) $35.43 ^ { \circ }$
D) $80.44 ^ { \circ }$
E) $60.33 ^ { \circ }$

Question

Given $a = 9 , b = 12 , \text { and } c = 7 ,$ , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places. 
A)$96.38 ^ { \circ }$
B) $48.19 ^ { \circ }$
C) $35.43 ^ { \circ }$
D) $80.44 ^ { \circ }$
E) $60.33 ^ { \circ }$

Quizplus · Accepted Answer

The Law of Cosines is given by $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $C$ is the angle opposite side $c$. To find angle $B$, we rearrange the formula to solve for $\cos(B)$: $\cos(B) = \frac{a^2 + c^2 - b^2}{2ac}$. Substituting $a = 9$, $b = 12$, and $c = 7$, we get $\cos(B) = \frac{9^2 + 7^2 - 12^2}{2 \cdot 9 \cdot 7}$. Calculating this gives $\cos(B) \approx -0.2143$, and taking the arccos gives $B \approx 96.38^\circ$.

Given a=9,b=12, and c=7,a = 9 , b = 12 , \text { and } c = 7 ,a=9,b=12, and c=7,

Given $a = 9 , b = 12 , \text { and } c = 7 ,$