Trigonometry
posted by Paul .
a flagpole 25 feet tall stands on a top of a building. from a point in the same horizontal plane with the base of the building. The angle of elevation of the top and the bottom are 61°30' and 56°20' respectively. How high is the building?

assuming the angles are to the flagpole
draw a diagram. If the distance from the building is x and the building has height h,
(h+25)/x = tan61°30'
h/x = tan56°20'
equating values of x, we get
(25+h)56°20' = h tan61°30'
1.50133(25+h) = 1.84177h
h = 110.25