Question

Amari is standing 50 feet from the base of a building. From where he stands, the angle formed between the top of the building and the ground at his feet is 60°.

Amari is standing 50 feet from the base of a building. From where he stands, the angle formed between the top of the building and the ground at his feet is 60 degrees. The angle between the building and the ground is a right angle.

How tall is the building?

50 ft
StartFraction 50 StartRoot 3 EndRoot Over 3 EndFraction ft
50 StartRoot 3 EndRoot ft
100 ft

Answer 1

Let the building height be h. With angle of elevation 60° and adjacent side 50 ft,

tan(60°) = h / 50.

Since tan(60°) = √3,

h = 50·√3 = 50√3 ft.

So the correct choice is 50√3 ft (≈ 86.6 ft).