Chapter 8.6, Problem 11WE

To determine

To find: the values of variables $w°$ and $v°$ .

Answer to Problem 11WE

The values of variables $w°$ and $v°$ are $106°$ and $37°$ respectively.

Explanation of Solution

Given:

The triangle is shown below:

  

Calculation:

In given triangle,

  $\angle A=\angle C=v°$

Hence, the triangle ABC is isosceles triangle.

Draw a perpendicular from vertex B as shown below:

  

Hence,

  $\begin{array}{c}AD=\frac{1}{2}AC\\ =\frac{1}{2}\left(16\right)\\ =8\end{array}$

In right triangle ADB ,

Angle $v°$ is calculated as follows:

  $\begin{array}{c}\cos v°=\frac{AD}{AB}\\ \cos v°=\frac{8}{10}\\ v°\approx 37°\end{array}$

In right triangle ABC ,

  $\begin{array}{l}\angle A+\angle B+\angle C=180°\left(\text{Sum}\text{of}\text{angles}\text{of}\text{triangle}\right)\\ v°+w°+v°=180°\\ 37°+w°+37°=180°\\ w°=106°\end{array}$

Hence, the values of variables $w°$ and $v°$ are $106°$ and $37°$ respectively.