Question

Construction A loading ramp 10 feet long that makes an angle of 18° with the horizontal is to be replaced by one that makes an angle of 12° with the horizontal. How long is the

new ramp?

Short answer

The new ramp is 14.86 feet long.

Step-by-step solution

Step 1. Given Information

A 10 ft loading ramp makes an ${18}^{\circ }$angle with the horizontal. It is being replaced by a loading ramp which makes localid="1649067956170" ${12}^{\circ }$angle with the horizontal.

Uselocalid="1649067960386" $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Step 2. Find the angle which completes the line 

$$\begin{gathered} \theta +18=180 \\ \theta ={162}^{\circ } \end{gathered}$$

Step 3. Finding length of ramp

By using

$$\begin{gathered} \frac{\sin 162}{l}=\frac{\sin 12}{10} \\ l\times \sin 12=10\times \sin 162 \\ l=\frac{10\times \sin 162}{\sin 12}=14.86feet \end{gathered}$$