SOLUTION: Angles of Depression/Elevation: From the top of a tower 83 feet high, a man observes that the angle of elevation of the top of a certain tree is 13 degrees and the angle of depress

Question 735545: Angles of Depression/Elevation: From the top of a tower 83 feet high, a man observes that the angle of elevation of the top of a certain tree is 13 degrees and the angle of depression of its base is 72 degrees. Find the height of the tree.''.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
tower = 83 ft
let the tree be x ft taller than the tower
Tree height = (83+x) ft
Let y be the distance between tree and tower

Tan 13 = x/y
y=x/ Tan 13.........................(1)
Tan 72 = 83/y
y= 83/tan 72.........................(2)
x/ tan 13 = 83/ tan 72
x= 83 * tan 13 / tan 72
x= 6,23 ft
Height of tree = 83+6.23= 89.23 feet

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