Question
CBSEENMA10008294

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Solution

Let height of the pedestal BD be h metres, and angle of elevation of C and D at a point A on the ground be 60° and 45° respectively.
It is also given that the height of the statue CD be 1.6 m
i.e.,    ∠CAB = 60°,
∠DAB = 45° and CD = 1.6m
In right triangle ABD, we have
tan space 45 degree space equals space BD over AB
rightwards double arrow space space space 1 space equals space straight h over AB
rightwards double arrow space space space AB thin space equals space straight h space space space space space space space space space... left parenthesis straight i right parenthesis
In right triangle ABC, we have
tan space 60 to the power of degree space equals space BC over AB
rightwards double arrow space space square root of 3 space equals space fraction numerator BD plus DC over denominator AB end fraction
rightwards double arrow space space square root of 3 space equals space fraction numerator straight h plus 1.6 over denominator AB end fraction
rightwards double arrow space space AB space equals space fraction numerator straight h plus 1.6 over denominator square root of 3 end fraction space space space space space space space space... left parenthesis ii right parenthesis

Comparing (i) and (ii), we get
straight h space equals space fraction numerator straight h space plus 1.6 over denominator square root of 3 end fraction
rightwards double arrow space space space square root of 3 space end root space straight h space equals space straight h space plus space 1.6
rightwards double arrow space space space square root of 3 space straight h space minus space straight h space equals space 1.6
rightwards double arrow space space space straight h left parenthesis square root of 3 minus 1 right parenthesis space equals space 1.6
rightwards double arrow space space space straight h space equals space fraction numerator 1.6 over denominator square root of 3 minus 1 end fraction straight x fraction numerator square root of 3 plus 1 over denominator square root of 3 plus 1 end fraction
rightwards double arrow space space space straight h space equals space fraction numerator 1.6 left parenthesis square root of 3 plus 1 right parenthesis over denominator 3 minus 1 end fraction
rightwards double arrow space space space straight h space equals space 0.8 open parentheses square root of 3 plus 1 close parentheses
Hence, the height of pedestal 

Sponsor Area

Some More Questions From Circles Chapter