Applications of Trigonometric Functions

Question

The angle of elevation to the top of a building changes from 28 degrees to 56 degrees as an observer advances 170 feet toward the building. Find the height of the building, x, to the nearest foot

Answer 1

We are solving for x = the height of the building.

Let d = the distance to the building when the angle of elevation to the top is 28°.

Then d – 170 is the distance to the building , observing from 170 ft closer, when the angle of elevation to the top is 56°.

x/d = tan(28°) and x/(d – 170) = tan(56°)

which means that

x = (d)tan(28°) = (d – 170)tan(56°) = (d)tan(56°) – 170tan(56°)

Add 170tan(56°) – (d)tan(28°) to both sides to get

(d)tan(56°) – (d)tan(28°) = d[tan(56°) – tan(28°)] = 170tan(56°)

Divide both sides by tan(56°) – tan(28°) to get

d = 170tan(56°)/[tan(56°) – tan(28°)]

Since x = (d)tan(28°) we can write

x = 170tan(28°)tan(56°)/[tan(56°) – tan(28°)] = 141 ft

Answer

The height of the building is 141 ft