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Question
If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower in the same straight line with it are complementary, find the height of the tower.
Solution
Let AC be the height of tower is h meters.
Given that: angle of elevation are `∠B=90°-θ`and ` ∠D=θ` and also`CD=4`m and`BC=9.m`.
Here we have to find height of tower.
So we use trigonometric ratios.
In a triangle, ADC
`tan θ=h/4`
Again in a triangle ,ABC
⇒` tan (90°-θ)=AC/BC`
⇒` cot θ=h/9`
`⇒ 1/tanθ=h/9`
put `tan θ=h/4`
`⇒ 4/h=h/9`
`⇒ h^2=36`
`⇒ h=6`
Hence height of tower is 6 meters.
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