Question

A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 112 feet from a building and 131 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth

Answer 1

The range finder is 112 feet from the building ( adjacent ) and 131 feet from the top of the building ( hypotenuse ).

We will use the Pythagorean theorem:

x² = 131² - 112²

x² = 17,161 - 12,544

x² = 4,617

x = √ 4,617

x = 67.948

The height of the building:

h = x + 3 = 67.948 + 3 = 70.948 ≈ 70.9 ft ( to the nearest tenth )