Bill determines that the angle of elevation to the top of a building measures 40°30'. if he walks 102 ft closer to the building, the measure of the new angle of elevation will be 50°20'. find the height of the building.

First, illustrate the given situation by drawing a right triangle. The building is one leg of the triangle, the distance from the building to Bill is the other leg. The angle of elevation is formed by the distance from Bill to the building and the hypotenuse of the triangle. 

Set up two equations:

tan (50°20') = y/ (x-102)

tan (40°30') = y/ (x)

Solve for x and y. y is the height of the building. 

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2