Question

a tree standing vertically on level ground casts a 118 foot long shadow. the angle of elevation from the end of the shadow to the top of the tree is 22.3 degrees. find the height of the tree to the nearest tenth of foot.

Answer 1

Since the situation forms a right triangle, we can apply trigonometric functions:

Tan a = opposite side/ adjacent side

Where:

a= angle = 22.3°

opposite side = x

adjacent side = 118

Replacing:

Tan 22.3° = x / 118

Solve for x

Tan 22.3 * 118 = x

x = 48.4 ft