Question

A person standing on top of a 11 11-foot high sand pile wishes to estimate the width of the pile. he visually locates two rocks on the ground below at the base of the sand pile. the rocks are on opposite sides of the sand pile, and he and the two rocks are in the same vertical plane. if the angles of depression from the top of the sand pile to each of the rocks are 28 ∘ 28∘ and 19 ∘ 19∘, how far apart are the rocks rounded to the nearest foot?

Answer 1

Refer to the diagram shown below.

The distance between the two rocks is (a + b).
By definition,
tan(28°) = 11/a
a = 11/tan(28°) = 20.688 ft
Similarly,
b = 11/tan(19°) = 31.9463 ft

The distance between the rocks is
20.688 + 31.9463 = 52.6343 ft

Answer: 53 ft (nearest foot)