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 )
Answer: h = 70.9 feet.