Question

Solve the triangle. Round your answers to the nearest tenth.Answer Options:A. m∠B=47, m∠C=28, b=24B. m∠B=47, m∠C=28, b=28C. m∠B=43, m∠C=32, b=28D. m∠B=46, m∠C=29, b=24

Answer 1

Therefore, for the given triangle:

`\begin{gathered} (37)/(sin(105))=(18)/(sin(C)) \\ sin(C)=(18*sin(105))/(37) \\ C=\sin^(-1)((18*sin(105))/(37)) \\ C=28° \end{gathered}`

For angle B, remember that all the intern angles of a triangle must add up to 180 degrees, then;

`\begin{gathered} B=180-105-28 \\ B=47° \end{gathered}`

Now, for side b:

`\begin{gathered} (b)/(sin47)=(37)/(sin105) \\ b=(37*sin47)/(sin105) \\ b=28 \end{gathered}`

Hence, the answer is B.