Question

A person 5.4 feet tall stands in line of a shadow cast from the top of the house. The shadow hits the top of the person's head, and continues until the shadow ends on the ground 2.4 feet from the person's shoes. The distance along the ground from the tip of the shadow to the house is 14.6 feet. Find the height of the house. Do not round your answer.

Answer 1

Refer to the diagram shown below.

Let h = the height of the building.

Because triangles ABC and ADE are similar (due to AAA), therefore
DE/BC = AD/AB
That is,
h/5.4 = 14.6/2.4
h/5.4 = 6.0833
h = 6.0833*5.4 = 32.8498 ft

Answer: The height of the house is 32.8498 ft