Question

A ramp is 150 feet long and rises 25 feet. What is the angle of elevation of the ramp?

Answer 1

First, draw a diagram to represent the situation.

Explanation:

We are looking for angle `theta`.

To determine which primary ratio we will use (sin, cos or tan), we have to determine the positions of the sides compared to our angle `theta`.

25 is opposite

150 is the hypotenuse

Using the acronym SOHCAHTOA, we realize that when we know opposite and hypotenuse, we use sin.

`sintheta = 25/150`

Isolate `theta`:

`theta = sin^-1(25/150)`

`theta = 9.59 = 10`

The ramp's angle of elevation measures 10 degrees.

Practice exercises:

1. A plane flies at an elevation of 2874 feet. It is at a distance of 9222 feet of the airport. Find:

a) The direct distance, assuming the plane stays at the same altitude, between its current location and the sky directly above the airport.

b) The angle of depression between the plane's current location and the airport.

Good luck!