Question

of the ratio of the height of the tower and the length of the shadow is √3:1 what is the angle of elevation of the sun
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Answer 1

Step-by-step explanation:

If the ratio of the height of a tower and the length of its shadow is √3 :1, then the angle of elevation of the Sun is 30º.

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Answer 2

Step-by-step explanation:

⋆ Diagram:-

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Given:-

• The ratio of the height of the tower and length of the shadow is √3 : 1.

To Find:-

• The angle of elevation of the sun.

Solution:-

Let AB be the height of the tower and

BC be the length of the shadow.

ATQ:-

Ratio of the height of tower and length of shadow is √3 : 1

$\sf \dfrac{AB}{BC} = \dfrac{\sqrt{3}}{1}$

In a right angled triangle.

$\sf \dfrac{Opposite \: side}{Adjacent \: side} = tan\theta$

So, In △ABC

$\sf \dfrac{AB}{BC} = tan\theta$

$\sf \dfrac{AB}{BC} = tan\theta$

$\sf \implies \dfrac{ \sqrt{3} }{1} = tan\theta$

$\sf \implies \sqrt{3} = tan\theta$

$\sf \implies tan60 ^{ \circ} = tan\theta$

$\sf \implies \theta = 60 ^{ \circ}$

$\underline{\boxed{\therefore \sf Angle \: of \: elevation \: of \: the \: sun = 60 ^{ \circ} }}$