Chapter 6, Problem 1CT

To determine

To find: The solution for the given triangle.

Answer to Problem 1CT

The value of angle $C$ is $46°$ and the lengths of the sides are $b=22.03$ and $a=13.07$ .

Explanation of Solution

Given:

The angles of the triangle are $A=36°$ and $B=96°$ value of the side $c=16$ .

Calculation:

The sketch for triangle with all the side labelled is shown in Figure 1

  

Figure 1

From the angle sum property the third angle of the triangle is,

  $C=180°-A-B$

Then,

  $\begin{array}{c}C=180°-36°-98°\\ =46°\end{array}$

Consider the law of sine is,

  $\begin{array}{l}\frac{b}{\sin B}=\frac{c}{\sin C}\\ b=\frac{c}{\sin c}\left(\sin B\right)\end{array}$

Then,

  $\begin{array}{c}b=\frac{16}{\sin 46°}\left(\sin 98°\right)\\ =22.03\end{array}$

Consider the law of sine is,

  $\begin{array}{l}\frac{a}{\sin A}=\frac{c}{\sin C}\\ a=\frac{c}{\sin c}\left(\sin A\right)\end{array}$

Then,

  $\begin{array}{c}a=\frac{16}{\sin 46°}\left(\sin 36°\right)\\ =13.07\end{array}$