Question

What is the angle of depression from the start of a 6-foot-high access ramp that ends at a point 40 feet away along the ground?

Answer 1

Answer:

8.53°

Step-by-step explanation:

Observe the attached image.

The ramp forms an alpha angle triangle with an opposite side of 6 ft and an adjacent side of 40 ft.

We know that the tangent of an angle is defined as:

$tan(\alpha) = \frac{opposite\ side}{adjacent\ side}$

So:

$tan(\alpha) = \frac{6}{40}$

To clear the angle we apply the inverse of the tangent (arctangent) on both sides of the equation:

$atan(tan(\alpha)) =atan(\frac{6}{40})$

$\alpha= atan(\frac{6}{40})\\\\\alpha = 8.53\°$