Chapter 11.7, Problem 29E

To determine

To find:

The surveyor from the bottom of the building.

Answer to Problem 29E

  $b=109.6ft$

Explanation of Solution

Given:

The building is on top of a hill

  $60ft$

The angle of elevation to the bottom measure is

  ${18}^0$

Concept used:

Using the law of sines formula

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

Calculation:

The red angle

  $\begin{array}{l}=90-42\\ =48\end{array}$

By using the law of sines formula

  $\begin{array}{l}\frac{60}{\sin \left(42-18\right)}=\frac{b}{\sin \left(48\right)}\\ \frac{60}{\sin \left(24\right)}=\frac{b}{\sin \left(48\right)}\\ \sin \left(48\right)\times \frac{60}{\sin \left(24\right)}=b\\ b=109.6ft\end{array}$

Darw the graph