Question

The headlights of an automobile are set such that the beam drops 3 in for each 32 ft in front of the car. What is the angle (give positive value) between the beam and the road in degrees ?

Answer 1

Answer:

0.4476 degrees.

Step-by-step explanation:

Let θ be the angle between the beam and the road. The given values form a right triangle with the distance that the beam drops ( h=3 in) being the side opposite to θ and the distance in front of the car (x=32 ft or x=384 in) being the side adjacent to θ.

Therefore, θ is given by:

$tan^{-1}(\theta) = \frac{h}{x}\\tan^{-1}(\theta) = \frac{3}{384}\\ tan^{-1}(\theta) = \frac{1}{128}\\\theta=0.4476^o$

The angle between the beam and the road is 0.4476 degrees.