Chapter 3, Problem 1P

A laser range finder records the distance from the laser to the base and from the laser to the top of a building as shown in Fig. P3.1. Find the angle $\theta$ and the height of the building.

To determine

The angle $\theta$ and the height of the building.

Answer to Problem 1P

The height of the building is 66.14 m and the angle $\theta$

$$ is $41.4°$.

Explanation of Solution

Given:

The given figure representing the building top and range finder is shown below.

Calculation:

Consider the below figure.

First calculate an angle $\theta$ ,

From the right angle triangle

$\cos \theta =\frac{\text{Adjecent side}}{\text{Hypotenuse}}$

$\begin{array}{l}\cos \theta =\frac{75}{100}\\ \theta ={\cos }^{-1}\left(\frac{75}{100}\right)=41.4°\end{array}$

Therefore the angle $\theta$

$$ is $41.4°$.

For the height of the building,

$\sin \theta =\frac{\text{opposite side}}{\text{Hypotenuse}}$

$\sin \left(41.4°\right)=\frac{h}{100}$

$0.6614=\frac{h}{100}$

$h=0.6614\times 100=66.14\text{m}$

Conclusion:

Thus, the height of the building is 66.14 m and the angle $\theta$

$$ is $41.4°$.