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Question
A statue 1.46m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the status 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 AC be the pedestal and BC be the statue such that BC = 1.46m.
We have:
∠ADC = 45° and ∠ADB = 60°
Let:
AC = hm and AD = xm
In the right ΔADC,we have:
`(AC)/(AD) = tan 45° = 1`
`⇒ h/x = 1`
⇒ h = x
Or,
x = h
Now, in the right ΔADB,we have:
`(AB)/(AD) = tan 60° = sqrt(3)`
`(h+1.46)/x = sqrt(3)`
On putting x = h in the above equation, we get
`(h+1.46)/h = sqrt(3)`
`⇒ h + 1.46 = sqrt(3)h`
`⇒ h( sqrt(3)-1) = 1.46`
`⇒ h = 1.46/( sqrt(3)-1) = 1.46/0.73 = 2m`
Hence, the height of the pedestal is 2 m.
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