Chapter 8.2, Problem 44AYU

To determine

Find the length of the ramp.

Answer to Problem 44AYU

  $\boxed{14.86ft}$

Explanation of Solution

Given information:

A loading ramp $10$ ft long that makes an angle angle of $12°$ with the horizontal. How long is new ramp?

Calculation:

  

Here,in oblique triangle $\Delta ABC$ ,

  $\angle ACB=12°,\angle ABD=18°,AB=10ft$

By using triangle property,

  $\begin{array}{l}\angle CBA+18°=180°,\\ \angle CBA=180°-18°\\ \angle CBA=162°\end{array}$

Using low of sine, we get

  $\frac{\sin B}{CA}=\frac{\sin C}{AB}$

Putting the values,

  $\begin{array}{l}\frac{\sin 162°}{CA}=\frac{\sin 12°}{10}\\ now,\\ CA=10\times \frac{\sin 162°}{\sin 12°}\\ CA=10\times \frac{0.30902}{0.20791}\\ CA=14.86304ft\end{array}$

Hence, the length of the ramp $\boxed{14.86ft}$ .