At a point on the ground 20 feet from a building, a surveyor observes the angle of inclination to the top of the building to be pi/3 radians. How tall is the building?

Question

asked Dec 1, 2021 80.2k views

1 Answer

Ryekayo · Answer 1 · 2021-12-07T14:43:01+0000

Answer:

34.64 ft

Explanation:

Distance from the building = 20 ft

Angle of inclination = π/3 radians

The tangent of the angle of inclination must equal the height of the building divided by the distance of the observer from the building:

$tan( \pi/3) = (h)/(20) \\h = 20*1.73205\\h=34.64\ ft$

The building is 34.64 ft tall