Question

Imagine you are standing 20 feet away from a tree that is 80 feet tall.

That angle that your feet make with the top of the tree is_?

Answer 1

The angle that the feet make with the top of the tree is approximately 76°

Explanation:

Since, the tree is generally assumed vertical with respect to the ground,

Let the line segment AB represents the tree ( A is top B is bottom ),

And, C represents the position of the feet,

Thus, angle B must be 90°,

Given,

AB = 80 feet,

BC = 20 feet,

We have to find out : ∠C,

We know that,

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

`\implies tan C = (80)/(20)`

`\implies tan C = 4`

`\implies \angle C = 75.9637565321\approx 76^(\circ)`

Hence, the angle that the feet make with the top of the tree is approximately 76°.

Answer 2

to find the angle take the arctan of the height divided by the base:

angle = arctan(80/20)

angle = 75.96

angle = 76 degrees