Question

a tree casts a shadow that is 24 feet in length. If the angle of elevation is 30 degrees, which of the following best represents the height of the tree?

Answer 1

13.85 feet

Explanation:

From question statement,we observe that tree together with its shadow makes right angle triangle.

Let the angle of elevation is ∅ whose value is given in statement.The tree casts a shadow which makes the base of triangle. We have to find the height of the tree which represents the perpendicular of triangle.

Hence, ∅ = 30° , base = 24 feet and perpendicular = ?

Since , we know that Tan∅ = perpendicular / base

putting given values in above formula,we get

Tan30° = perpendicular / 24

perpendicular = Tan30° ×24

perpendicular = .5773×24

perpendicular = 13.85 feet

Hence,13.85 feet is the height of the tree.

Answer 2

13.856 feet

Explanation:

The height of the tree and its shadow forms a right angle. Together with the line joining the pit of the shadow and the tree make a right triangle.

We can use the trigonometric ratio tangent to find its height.

tan = opposite/adjacent

tam 30° = x/24

height = 24 × tan 30°

= 24 ×0.57735

= 13.856 feet