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Question

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

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Solution

Let AB be the building and CD be the tower such that BDE=30,BCA=60 and AB = 60 m

Let CA = DE = x metres.



From right ΔCAB, we have

CAAB=cot 60=13

x60=13x=60×13

x=60×13×33=203

CA=DE=203

From right ΔBED, we have

BEDE=tan 30=13BE203=13 [using (i)]

BE=203×13m=20 m

CD=AE=ABBE=60 m20 m40 m

Hence the height of the tower is 40 m

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