Question

7. From a point on the horizontal plane the tangent of the angle of elevation of the top of a minar is 5/3
On moving 32 metres towards the foot of the minar, the tangent of the angle of elevation of
3
the top becomes 5/2- Find the height of the minar.​

Answer 1

The height of minar is 160 meters

Step-by-step explanation:

Please refer attachment for figure.

Let h meter of the height of minar.

From a point on the horizontal plane the tangent of the angle of elevation of the top of a minar is 5/3

In ΔABC, ∠ABC = 90°

$\tan \angle A=\dfrac{BC}{AB}$

$\dfrac{5}{3}=\dfrac{h}{32+x}$----------(1)

On moving 32 metres towards the foot of the minar, the tangent of the angle of elevation of  the top becomes 5/2

In ΔBCD, ∠DBC = 90°

$\tan \angle D=\dfrac{BC}{DB}$

$\dfrac{5}{2}=\dfrac{h}{x}$--------------(2)

Using eq(1) and eq(2) solve for h

$\dfrac{5}{3}=\dfrac{h}{32+\dfrac{2h}{5}}$

$160+2h=3h$

$h=160$

Hence, the height of minar is 160 meters

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