Chapter 8.5, Problem 3CYU

To determine

The height of the disco ball.

Answer to Problem 3CYU

  $14.2\text{feet}$

Explanation of Solution

Given:

  

Calculation:

The figure can be drawn as:

  

The height of the disco ball will be:

  $\begin{array}{l}\tan 40=\frac{x}{GH}\\ GH=\frac{x}{\tan 40}\\ GA+AH=\frac{x}{\tan 40}\\ 5+AH=\frac{x}{\tan 40}\\ \text{and}\\ \tan 50=\frac{x}{AH}\\ AH=\frac{x}{\tan 50}\\ \text{Therefore,}\\ 5=\frac{x}{\tan 40}-\frac{x}{\tan 50}\\ 5=\left(\frac{x}{\tan 40}-\frac{x}{\tan 50}\right)1\\ x=\frac{5}{\frac{1}{\tan 40}-\frac{1}{\tan 50}}\\ x=14.2\text{feet}\end{array}$