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Question
If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is
Options
ab
\[\sqrt{ab}\]
\[\frac{a}{b}\]
\[\sqrt{\frac{a}{b}}\]
Solution
Let h be the height of tower AB.
Given that: angle of elevation of top of the tower are `∠D=θ`and .`∠C=90°-θ`
Distance`BC=b` and `BD=a`
Here, we have to find the height of tower.
So we use trigonometric ratios.
In a triangle, ABC
`tan D=(AB)/(BC)`
`⇒ tan (90°-θ)=h/b`
`⇒ cotθ=h/b`
Again in a triangle ABD,
`tan D=(AB)/(BD)`
`⇒ tan θ=h/a`
`⇒1/cot θ=h/a`
⇒ `b/h=h/a`
`⇒h^2=ab`
`⇒ h=sqrt(ab)`
Put `cotθ=h/b `
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