Question

A boy standing on a level ground, sees the top of a tower at an elevation of 40°.After walking 30 metres towards the tower, he sees it at an elevation of 80°.Calculate the height of the tower.

Answer 1

Given:

A boy standing on the level ground sees the top of a tower at an elevation of 40°.

After walking 30 metres towards the tower, he sees it at an elevation of 80°.

To find:

The height of the tower

Solution:

To solve the given problem we will use the following formula of trigonometric ratios:

$\boxed{\bold{tan\:\theta = \frac{Perpendicular}{Base} }}$

Referring to the figure, we have

"AB" → height of the tower

"CD" → distance moved by the boy towards the tower = 30 m

"∠ADC" = 40° → angle of elevation of the top of the tower

"∠ACB" = 80° → angle of elevation of the top of the tower after moving 30 m towards the tower

Considering Δ ABC, we have

θ = 80°

Perpendicular = AB

Base = BC

∴ $tan \:80\° = \frac{AB }{BC}$

$\implies 5.671 = \frac{AB}{BC}$

$\implies AB = BC \times 5.671$ ....... (i)

Considering Δ ABD, we have

θ = 40°

Perpendicular = AB

Base = BC + CD

∴ $tan \:40\° = \frac{AB }{BC + 30}$

$\implies 0.839 = \frac{AB}{BC+ 30}$

$\implies AB = 0.839BC + 25.17$ ....... (ii)

Comparing equations (i) & (ii), we get

$\implies BC \times 5.671 = 0.839BC + 25.17$

$\implies 5.671 BC - 0.839BC = 25.17$

$\implies 4.832BC = 25.17$

$\implies BC = \frac{25.17}{4.832}$

$\implies BC = 5.2 \:m$

On substituting the value of BC in eq. (i), we get,

$AB = 5.2 \times 5.671 = \bold{29.48\:m}$

Thus, the height of the tower is 29.48 m.

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Also View:

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