Question

In the triangle below, b= If necessary, round your answer to twodecimal places.

Answer 1

Given

The triangle,

To find:

The value of b.

Explanation:

It is given that,

That implies,

By using sine law,

$\frac{a}{\sin A}=\frac{b}{\sin B}$

Since the sum of the angles in a triangle is 180°.

Then,

$\begin{gathered} \angle B=180-(32.5+26.8) \\ =180-59.3 \\ =120.7 \end{gathered}$

Therefore,

$\begin{gathered} \frac{25}{\sin(32.5)}=\frac{b}{\sin(120.7)} \\ b=\frac{25\times\sin(120.7)}{\sin(32.5)} \\ b=\frac{21.496}{0.537} \\ b=40.008 \\ b=40.01 \end{gathered}$

Hence, the value of b is 40.01.