Chapter 12.7, Problem 4P

To determine

To determine the length of sides.

Answer to Problem 4P

The length of side is 39.1 in.

Explanation of Solution

Given information :

Two sides meet at angle of ${35}^{\circ }$

Side is 16in.

Here two equalangle is,

  $\left({180}^{\circ }-{35}^{\circ }\right)={145}^{\circ }$

Hence the two equal angles are $\frac{{145}^{\circ }}{2}={72.5}^{\circ }$

We have to find the side opposite to the angle ${72.5}^{\circ }$

Now according to law of sines,

In any triangle ABC,

  

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

Hence,

  $\begin{array}{l}\frac{16}{\sin {35}^{\circ }}=\frac{b}{\sin {72.5}^{\circ }}\\ b=\frac{\sin {72.5}^{\circ }\times 16}{\sin {35}^{\circ }}\\ b=39.1\end{array}$

Hence the length of side is 39.1 in.