Question

the length of the Shadow of a tower is 9 metres when the sun's angle of elevation is 30digree.let us write by calculating the height of a tower.

Answer 1

Given:

The length of the shadow of the tower = 9 m

The sun's angle of elevation = 30°

To find:

The height of a tower

Solution:

We will use the following trigonometric function of a triangle to solve the given problem:  

$\boxed{\boxed{\bold{tan\: \theta = \frac{Opposite\:Side}{Adjacent\:Side} }}}$

 

Here from the figure attached below, in Δ ABC, we have,

θ = 30°

Opposite Side / Perpendicular = AB = height of the tower

Adjacent Side = BC = 9 m

∴   $tan\: 30 = \frac{AB}{BC}$

by substituting the tan 30° = $\frac{1}{\sqrt{3} }$  and BC = 9 m

⇒   $\frac{1}{\sqrt{3}} = \frac{AB}{9}$

⇒   $AB = \frac{9}{\sqrt{3}}$

⇒   $AB = \frac{9}{1.732}$

⇒ $\bold{AB = 5.19\:m}$

Thus, the height of a tower is 5.19 m.

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