A tower AB leans towards west marking an angle - with the vertical- The angular elevation of B- the top most point of the tower is - as observed from a point C due east of A at a distance -d- from A- If the angular elevation of B from a point D due east of C at a distance 2d from C is r- then 2tan- can be given as

The correct option is C 3β γ By m n theorem at C (d + 2d) β = dγ 2d (90^∘ + α) 3dβ = dγ + 2d tanα ⇒ 3β = γ + 2tanα ∴ ...

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Byju's Answer

Standard X

Mathematics

Calculating Heights and Distances

A tower AB ...

Question

A tower $A B$ leans towards west marking an angle $α$ with the vertical. The angular elevation of $B$ , the top most point of the tower is $β$ as observed from a point $C$ due east of $A$ at a distance $^{'} d^{'}$ from $A$ . If the angular elevation of $B$ from a point $D$ due east of $C$ at a distance $2 d$ from $C$ is $r$ , then $2 tan α$ can be given as

3 cot β - 2 cot γ

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3 cot γ - 2 cot β

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3 cot β - cot γ

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cot β - 3 cot γ

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Solution

The correct option is C $3 cot β - cot γ$
By $m - n$ theorem at $C$
$(d + 2 d) cot β = d cot γ - 2 d cot (90^{\circ} + α)$
$3 d cot β = d cot γ + 2 d tan α$
$\Rightarrow 3 cot β = cot γ + 2 tan α$
$∴ 2 tan α = 3 cot β - cot γ$

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The correct option is C 3cotβ−cotγBy m−n theorem at C(d+2d)cotβ=dcotγ−2dcot(90∘+α)3dcotβ=dcotγ+2dtanα⇒3cotβ=cotγ+2tanα∴2tanα=3cotβ−cotγ

The correct option is C $3 cot β - cot γ$
By $m - n$ theorem at $C$
$(d + 2 d) cot β = d cot γ - 2 d cot (90^{\circ} + α)$
$3 d cot β = d cot γ + 2 d tan α$
$\Rightarrow 3 cot β = cot γ + 2 tan α$
$∴ 2 tan α = 3 cot β - cot γ$