Question

A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 105 feet from a building and 121 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth.

Answer 1

Answer:

The height of the building is 63 ft

Step-by-step explanation:

To solve this, we should note that the shape made by the range finder and the top and bottom of the building is a triangle.

Let the angle subtended by the range finder be $\theta$

The height of the building can be got by Pythagoras theorem which shows

$hyp^{2} = opp^{2} + adj^{2}$

$121^{2}= 105^{2} + opp ^{2}$

$opp^{2}=121^{2}-105^{2}=3616$

$opp=\sqrt{3616} =60.133 \approx 60ft$

hence the height of the building is 3 ft + 60 ft = 63 ft