Math Trigonometry Help

Question

To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 38°. From a point that is 200 feet closer to the building, the angle of elevation (at ground level) to the top of the building is 48°. If we assume that the street is level, use this information to estimate the height of the building.

Note that I don't think it's trying to find "h" more like a big triangle trying to find side "a".

Answer 1

38 degree angle from ground to top of the building

but 48 degree angle from 200 feet closer to the building base to top of the building

the height of the building = about 527 feet

construct 2 right triangles

both have side a = building height. "a" means altitude.

base for 38 degree angle triangle is x+200

base for 48 degree angle triangle is x

tan38 = a/(x+200) = about .781

tan48 = a/(x)= about 1.111

a = 1.111x = .781(x+200)

(1.111-.781)x = .781(200)

x = about 156.2/.3293 = about 474.3

a = 1.111x = about 1.111(474.3) = about 526.95

Building height = about 527 feet