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

8.53°

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) = (opposite\ side)/(adjacent\ side)`

So:

`tan(\alpha) = (6)/(40)`

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

`atan(tan(\alpha)) =atan((6)/(40))`

`\alpha= atan((6)/(40))\\\\\alpha = 8.53\°`