Chapter 8.1, Problem 56AYU

Directing a Laser Beam A laser beam is to be directed through a small hole in the center of a circle of radius 10 feet. The origin of the beam is 35 feet from the circle (see the figure). At what angle of elevation should the beam be aimed to ensure that it goes through the hole?

To determine

To find: The angle of elevation of laser beam.

Answer to Problem 56AYU

Angle of elevation is $\text{15}{\text{.95}}^{\circ }$.

Explanation of Solution

Given:

From the figure we can say that height of the small hole is 10 ft that is opposite side and the distance from the laser beam to the base of the small hole is 35 ft that is adjacent side.

Formula used:

$\tan \theta \text{ = }\frac{\text{opposite side}}{\text{adjacent side}}$

Calculation:

If opposite side and adjacent sides known we can use the $\tan$ for finding the elevation of the laser beam.

So $\tan \theta \text{ = }\frac{\text{opposite side}}{\text{adjacent side}}$.

$\tan \theta \text{ = }\frac{10}{35}$

$\theta {\text{ = tan}}^{-1}\left(\frac{2}{7}\right)$

$\theta =\text{ 15}{\text{.95}}^{\circ }$

so angle of elevation is $\text{15}{\text{.95}}^{\circ }$.