To estimate the height of a building.

Question

How would I go about solving this equation? If possible, please explain in details how you solved it.

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 36 deg . 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 57 deg If we assume that the street is level, use this information to estimate the height of the building.

Answer 1

construct 2 right triangles. one has 36 degrees opposite the height of the building

a 2nd right triangle is 200 feet closer with an angle to the building top of 57 degrees

let b = height of the building

x = distance from the 2nd student to the bottom of the building

b=xtan57 = (x+200)tan36

x = 200tan36/(tan57-tan36) = about 178.66

b = 178.66tan57 = about 275.12 feet high