Question

A 15 foot flagpole is mounted on top of a school building. If the top of the flagpole forms a 31° angle with the ground 50 ft from the base of the building, about how tall is the school building?

28 feet <-My answer
15 feet
30 feet <-second choice
11 feet

Answer 1

assuming the building is of height h, and the flag pole is right at the edge of the roof, then

(15+h)/50 = tan 31°
15+h = 50*0.6 = 30
h = 15

If the tree is x feet back from the roof, then

(15+h)/(x+50) = tan 31°
h+15 = .6x + 30
h = 15 + .6x

So, any height greater than 15 is a possible answer, depending on how far back the pole is from the building wall.

I think I'd still go with 15 feet.