From a point on the ground the angle of elevation of top of a tower is - On moving -a- meter towards the tower- the elevation changes to - The height of the tower is-

The correct option is D a tan α tan βtan β tan α REF.ImageIn AOC , tanα =h/a+x⇒ (a+x)tanα =h ⇒ x=h a tanα/tanα ___ (1)In BOC ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios Using Right Angled Triangle

From a point ...

Question

From a point on the ground the angle of elevation of top of a tower is $α$ . On moving 'a' meter towards the tower, the elevation changes to $β$ . The height of the tower is:

\frac{t a n β - t a n α}{a t a n α t a n β}

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\frac{a (t a n β - t a n α)}{t a n α t a n β}

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\frac{a t a n α - t a n β}{t a n α - t a n β}

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\frac{a t a n α t a n β}{t a n β - t a n α}

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Solution

The correct option is D $\frac{a t a n α t a n β}{t a n β - t a n α}$
REF.Image
In $△ A O C$ ,
$t a n α = \frac{h}{a + x} \Rightarrow (a + x) t a n α = h$
$\Rightarrow x = \frac{h - a t a n α}{t a n α}$ _ (1)
In $△ B O C$
$t a n β = \frac{h}{x} \Rightarrow x = \frac{h}{t a n β}$ _ (2)
From (1) & (2)
$\frac{h}{t a n β} = \frac{h}{t a n α} - a$
$h [\frac{1}{t a n β} - \frac{1}{t a n α}] = - a$
$h = \frac{a}{[\frac{1}{t a n α} - \frac{1}{t a n β}]}$
$h = \frac{a t a n α t a n β}{t a n β - t a n α}$

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A vertical tower stands on the horizontal ground and is surmounted by a vertical flagstaff of height 'h' metre. At a point on the ground, the angle of elevation of the bottom of the flagstaff is $α$ and that of the top of the flagstaff is $β$ . The height of the tower is ___ m.

A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively $α a n d β$ . Prove that the height of the top from the ground is $\frac{(b - a) t a n α t a n β}{t a n α - t a n β}$ .

Q. Prove that height of the tower =

\frac{α t a n β t a n α}{t a n β - t a n α}

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From a point on the ground the angle of elevation of top of a tower is α. On moving 'a' meter towards the tower, the elevation changes to β. The height of the tower is:

The correct option is D atanαtanβtanβ−tanαREF.ImageIn △AOC,tanα=ha+x⇒(a+x)tanα=h⇒x=h−atanαtanα ___ (1)In △BOCtanβ=hx⇒x=htanβ ___ (2)From (1) & (2)htanβ=htanα−ah[1tanβ−1tanα]=−ah=a[1tanα−1tanβ]h=atanαtanβtanβ−tanα

From a point on the ground the angle of elevation of top of a tower is $α$ . On moving 'a' meter towards the tower, the elevation changes to $β$ . The height of the tower is: