Chapter 8.2, Problem 51AYU

To determine

To find: The length of the awning.

Answer to Problem 51AYU

The length of the awning is $38.48\text{in}$ .

Explanation of Solution

Given information:

The given figure is,

  

Consider the following figure,

  

From the figure, calculate the value of $x$ as,

  $\begin{array}{l}\tan 25°=\frac{x}{\left(88-h\right)}\\ x=\left(88-h\right)\tan 25°\end{array}$

From the figure, calculate the value of $h$ as,

  $\begin{array}{l}h=\frac{x}{\tan 50°}\\ h=\frac{\left(88-h\right)\tan 25°}{\tan 50°}\\ h=24.74\text{in}\end{array}$

The length of the awning is calculated as,

  $\begin{array}{l}\text{cos}50°=\frac{h}{L}\\ \text{cos}50°=\frac{24.74}{L}\\ L=38.48\text{in}\end{array}$

Therefore, the length of the awning is $38.48\text{in}$ .