Question

An engineer is surveying a building with a device that is 5 feet above the ground. He is 50 feet from the building and is looking with an angle of elevation of 50°. How tall is the building?

Answer 1

1. Check the sketch of the problem.

2. In right triangle DCE,

 $tan50= \frac{EC}{DC}= \frac{x}{50}$

tan 50 can be found to be 1.19 using a scientific calculator or other software.

$1.19=\frac{x}{50}$

x=1.19*50=59.5 (feet)

3. The height of the building is 59.5+5=64.5 (feet)

Answer: 64.5 (feet)