Question

A cable runs from the top of a building to a point on the ground 60.3 feet from the base of the building. If the cable makes and angle of 33.7˚ with the ground (see figure), find the following: a. Find the height of the building. Round your answer to the nearest foot. b. Without using your answer from part a, find the length of the cable. Round your answer to the nearest foot.

Answer 1

Part A:

Given that the cable runs from the top of a building to a point on the ground 60.3 feet from the base of the building and that the cable makes and angle of 33.7˚ with the ground.

Let the height of the building be h, then

$\tan33.7^o= \frac{h}{60.3} \\ \\ \Rightarrow h=60.3\tan33.7^o \\ \\ \approx40\, feet.$



Part B:

Given that the cable runs from the top of a building to a point on the ground 60.3 feet from the base of the building and that the cable makes and angle of 33.7˚ with the ground.

Let the length of the building be l, then

$\cos33.7^o= \frac{60.3}{l} \\ \\ \Rightarrow l=\frac{60.3}{\cos33.7^o} \\ \\ \approx72\, feet.$