Question

A statue, 1.6 m tall, stands on a top of pedestal, from a point on the ground, the angle of elevation of the top of 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.

Answer 1

Let AB be the statue, BC be the pedestal, and D be the point on the ground from where the elevation angles are to be measured.

In ΔBCD,

`("BC")/("CD")` = tan 45°

`("BC")/("CB")` = 1

BC = CD

In ΔACD,

`("AB"+"BC")/("CD")` = tan 60°

`("AB"+"BD")/("BC") = sqrt3`

`1.6+"BC" = "BC"sqrt3`

`"BC"(sqrt3-1) = 1.6`

BC = `((1.6)(sqrt(3)+1))/((sqrt(3)-1)(sqrt(3)+1))`

= `(1.6(sqrt(3)+1))/((sqrt(3))^2-(1)^2)`

= `(1.6(sqrt3+1))/2`

= `0.8(sqrt3+1)`

Therefore, the height of the pedestal is 0.8 `(sqrt3+1)` m.