Question

The headlights of an automobile are set such that the beam drops 4.00 in for each 22.0 ft in front of the car. What is the angle between the beam and the road?

Answer 1

Given:

Beam drops at 4.00in

The distance between car and point is 22 ft

Find-:

The angle between beam and road is:

Sol:

Convert "inch" into ft.

`1\text{ in=0.0833 ft}`

So the 4 in is.

`\begin{gathered} 1\text{ in =0.0833 ft} \\ \\ 4*1\text{ in=4}*0.0833ft \\ \\ 4\text{ in=0.3332 ft} \end{gathered}`

Use the property of triangle is:

`\tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}}`

`\begin{gathered} \tan\theta=(0.3332)/(22) \\ \\ \tan\theta=0.015145 \\ \\ \theta=\tan^(-1)(0.015145) \\ \\ \theta=0.868 \end{gathered}`

So the angle is 0.868