SOLUTION: The angle of elevation from the top of a small building to the top of a nearby taller building is 52degrees, while the angle of depression to the bottom is 18degrees. If the smal

Question 916954: The angle of elevation from the top of a small building to the top of a nearby taller building is 52degrees, while the
angle of depression to the bottom is 18degrees. If the smaller building is 32 meters high, find the height of the
taller building.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the taller building be x m more than the smaller
Height of taller building = (x+32)
let the distance between them be y

The angle of elevation from the top of a small building to the top of a nearby taller building is 52degrees,
tan 52 = x/y
y= x/tan 52..............................(1)
while the angle of depression to the bottom is 18degrees.
so angle of elevat ion from bottom of taller building to the top of smaller building = 18 deg
tan 18 = 32/y
y=32/tan 18...............................(2)
from (1) & (2)
x/tan 52 = 32/tan 18
x= tan 52 *32/tan 18
x= 126 m
Height of taller building = 126+32= 158 m

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