SOLUTION: Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24�, and the angle of depre

Question 1087601: Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24�, and the angle of depression to the bottom of the taller building is 35�. How tall is each building?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24�, and the angle of depression to the bottom of the taller building is 35�. How tall is each building?

Solution:
Let the top and bottom of the taller building be points T and B respectively.
Let the top of the shorter building be the point S.
Finally, let the point on the taller building at the same elevation as the top of the shorter building be M.
Then TMS forms a right triangle, with base MS=200', and angle MST=24°
The length mMT=MStan(24°)=89.0'
Similarly for right triangle MSB, the length mMB=MS*tan(35°)=140.0'
Total height of taller building = BT=MB+BT=89.0+140.0=229'
Height of shorter building = BT = 140'

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