Chapter 12.8, Problem 12WE

To determine

Solve the triangle which has $b=15,c=14.5\text{ and }\angle C=70°$ .

Answer to Problem 12WE

  $a=8.53,\angle A=33.6°\text{ and }\angle B=76.4°$

Explanation of Solution

Given information: The given measurements of triangle are $b=15,c=14.5\text{ and }\angle C=70°$ .

Calculation: Since the given triangle has $b=15,c=14.5\text{ and }\angle C=70°$ . Therefore by sine formula,

  $\begin{array}{c}\frac{b}{\sin B}=\frac{c}{\sin C}\\ \frac{15}{\sin B}=\frac{14.5}{\sin 70}\\ \sin B=\frac{15\sin 70}{14.5}\\ B={\sin }^{-1}\left(0.97209\right)\\ B=76.4°\end{array}$

Since $\angle C=70.0°\text{ and }\angle B=76.4°$ therefore third angle is $\angle A=33.6°$ .

Again by sine formula,

  $\begin{array}{c}\frac{a}{\sin A}=\frac{c}{\sin C}\\ \frac{a}{\sin 33.6}=\frac{14.5}{\sin 70}\\ a=\frac{14.5\left(\sin 33.6\right)}{\sin 70}\\ a=8.53\end{array}$

Hence the given triangle has $a=8.53,\angle A=33.6°\text{ and }\angle B=76.4°$ .