Given a = 10,b = 12,and c = 8,use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places.
A)82.82°
B)55.77°
C)41.41°
D)80.44°
E)60.33°

Question

Given a = 10,b = 12,and c = 8,use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. ​
A)82.82°
B)55.77°
C)41.41°
D)80.44°
E)60.33°

Quizplus · Accepted Answer

The Law of Cosines formula is $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $C$ is the angle opposite side $c$. To solve for angle $B$, rearrange the formula to solve for $\cos(B)$: $\cos(B) = \frac{a^2 + c^2 - b^2}{2ac}$. Substituting the given values, $\cos(B) = \frac{10^2 + 8^2 - 12^2}{2 \cdot 10 \cdot 8}$, which simplifies to $\cos(B) = \frac{100 + 64 - 144}{160} = \frac{20}{160} = \frac{1}{8}$. Using a calculator to find $B$, we get $B \approx 82.82^\circ$.

Given a = 10,b = 12,and C = 8,use the Law