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Circles

Question
CBSEENMA10008318
Wired Faculty App

From the top of a building 60 m high the angles of depression of the top and the bottom of tower are observed to be 30° and 60°. Find the height of the tower.

Solution
Let AC be the tower and BE be the building. Let height of the tower be h m. It is given that the angles of depression of the top C and bottom A of the tower, observed from top of the building be 30° and 60° respectively.

In right triangle CDE, we have
tan space 30 degree space space equals space DE over CD rightwards double arrow space space space fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator 60 minus straight h over denominator CD end fraction space space space space space space space space space space space space left square bracket space DE space equals space BE space minus space BD space equals space BE space minus space AC space right square bracket rightwards double arrow space space space CD space equals space square root of 3 left parenthesis 60 minus straight h right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis straight i right parenthesis
In right triangle ABE, we have
tan space 60 degree space equals space BE over AB rightwards double arrow space space space space square root of 3 space equals space 60 over CD space space left parenthesis AB space equals space CD right parenthesis rightwards double arrow space space space space CD space equals space fraction numerator 60 over denominator square root of 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis
Comparing (i) and (ii), we get
square root of 3 left parenthesis 60 minus straight h right parenthesis space equals space fraction numerator 60 over denominator square root of 3 end fraction rightwards double arrow space space 3 space left parenthesis 60 minus straight h right parenthesis space equals space 60 rightwards double arrow space space 180 minus 3 straight h equals 60 rightwards double arrow space space space 3 straight h space equals space 120 rightwards double arrow space space space space straight h space space equals space 40
Hence, the height of the tower is 40 m.

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O1 and O2 of the object at A?

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