Question:
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 degree and from the same point the angle of elevation of the top of the pedestal is 45 degree . Find the height of the pedestal.
Answer:
From triangle BCD
tan45 = BC/CD
=> 1 = BC/CD
=> CD = BC
Again triangle ACD
tan60 = AC/CD
=> √3 = (AB + BC)/CD
=>√3*CD = AB + BC
=> √3BC = 1.6 + BC
=> √3BC - BC = 1.6
=> (√3 - 1)BC = 1.6
=> BC = 1.6/ (√3 - 1)
=> BC ={1.6* (√3 + 1)}/{(√3 - 1)*(√3 + 1)}
=> BC ={1.6* (√3 + 1)}/2
=> BC = 0.8 *(√3 + 1)
So height of pedestal is 0.8 *(√3 + 1)
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