Chapter 6.6, Problem 17E

To determine

To find: Thesolution of the triangle.

Answer to Problem 17E

The triangle have $a=193.34$ , $A=83.7°$ , and $C=56.30°$

Explanation of Solution

Given information:

The given sidesand angles of the triangle are,

  $\begin{array}{l}B=40°\\ c=162\\ b=125\end{array}$

Concept used:

Law of Sine:

If ABC is a triangle with sides $a$ , $b$ , and $c$ , then

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

Using Sine formula to calculate the angle $C$ of triangle ABC is.

  $\begin{array}{l}\frac{b}{\sin B}=\frac{c}{\sin C}\\ \frac{125}{\sin {40}^{\circ }}=\frac{162}{\sin C}\\ \sin C=\frac{162\times 0.642}{125}\\ C={56.30}^{\circ }\end{array}$

The angle $A$ of triangle is calculated as

  $\begin{array}{l}A+B+C=180°\\ A+40°+56.30°=180°\\ A=83.7°\end{array}$

The side $a$ of triangle is calculated as,

  $\begin{array}{l}\frac{a}{\sin A}=\frac{b}{\sin B}\\ \frac{a}{\sin {83.7}^{\circ }}=\frac{125}{\sin {40}^{\circ }}\\ a=\frac{125\times 0.993}{0.642}\\ a=193.34\end{array}$

Therefore, the triangle have $a=193.34$ , $A=83.7°$ , and $C=56.30°$ .