Chapter 12.7, Problem 3P

To determine

To determine the length of base.

Answer to Problem 3P

The base is 55.9 cm

Explanation of Solution

Given information :

Two angles are given ${23}^{\circ },{23}^{\circ }$

Equal side is 27 cm.

According to the properties of triangle, shortest side is always opposite to shortest angle and longest side is always opposite to largest angle.

Here third angle is,

  $\left({180}^{\circ }-{23}^{\circ }-{23}^{\circ }\right)={134}^{\circ }$

We have to find the side opposite to the angle ${134}^{\circ }$

Now according to law of sines,

In any triangle ABC,

  

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

Hence,

  $\begin{array}{l}\frac{27}{\sin {23}^{\circ }}=\frac{b}{\sin {134}^{\circ }}\\ b=\frac{\sin {134}^{\circ }\times 27}{\sin {23}^{\circ }}\\ b=49.7\end{array}$

Hence the base is 55.9 cm