From an unknown distance, the angle of elevation to the top of a building is 17 degrees

Question

 At some point, 50 feet closer to the base of the building, the angle of elevation is 31∘.

Calculate the height of the building. Include a diagram with your work.

Answer 1

let h= height of building

x = distance to the building after moving 50 feet closer

h/x = tan31 = about tan30 = .6

h/(50+x) = tan17 = close to .3

h= .6x = 15 + .3x

.3x = 15

x = 15/.3 = 50 degrees

h=.6x = .6(50) = 30 feet tall