Chapter 13, Problem 13SGR

To determine

To find:The length of the ramp off

Answer to Problem 13SGR

Length of ramp off $=c=8.8$ feet

Explanation of Solution

Given information:

  $\begin{array}{l}A={20}^0\\ C={90}^0\\ a=3\end{array}$

Concept:

Law of sines

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

Given

  $\begin{array}{l}A={20}^0\\ C={90}^0\\ a=3\end{array}$

Diagram of given situation is

  

We know

Using law of sines

We get

  $\begin{array}{l}\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\ \Rightarrow \frac{\sin {20}^0}{3}=\frac{\sin B}{b}=\frac{\sin {90}^0}{c}\end{array}$

Taking first and last terms

We get

  $\begin{array}{l}\Rightarrow \frac{\sin {20}^0}{3}=\frac{\sin {90}^0}{c}\\ \Rightarrow c=\frac{3\sin {90}^0}{\sin {20}^0}\\ \Rightarrow c=\frac{3\left(1\right)}{0.342}\\ \Rightarrow c=8.8\end{array}$

Therefore,

Length of ramp off $=c=8.8$ feet