Chapter 8.6, Problem 9WE

To determine

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

Answer to Problem 9WE

The values of variables x and $v°$ are $9$ and $63.25°$ respectively.

Explanation of Solution

Given:

The triangle is shown below:

  

Calculation:

In given triangle,

  $AB=BC=10$

Hence, the triangle ABC is isosceles triangle.

Hence,

  $\begin{array}{c}AD=\frac{1}{2}AC\\ =\frac{1}{2}\left(9\right)\\ =4.5\end{array}$

In right triangle ADB ,

Angle $v°$ is calculated as follows:

  $\begin{array}{c}\cos v°=\frac{AD}{AB}\\ \cos v°=\frac{4.5}{10}\\ v°=63.25°\end{array}$

Side $x$ is calculated as follows:

  $\begin{array}{c}\sin v°=\frac{BD}{AB}\\ \sin 63.25°=\frac{x}{10}\\ \frac{x}{10}=0.893\\ x\approx 9\end{array}$

Hence, the values of variables x and $v°$ are $9$ and $63.25°$ respectively.