If a tower $30\ m$ high, casts a shadow $10\sqrt{3} \ m$ long on the ground, then what is the angle of elevation of the sun ?

Academic Mathematics NCERT Class 10

Given: Height of the tower$=30\ m$ length of the shadow$=10\sqrt{3} m\ $

To do: To find the angle of the elevation of the sun.

Solution:

Angle of equation of sun$=\angle GST=\theta $

Height of lower $TG=30\ m$

Length of shadow $GS\ =10\sqrt{3} \ m$

$\vartriangle TGS$ is a right angled triangle,

$\therefore tan\theta =\frac{30}{10\sqrt{3}} =\frac{3}{\sqrt{3}} =\sqrt{3}$

As known $tan60^{o}=\sqrt{3}$

$\therefore \ \theta =60^{o}$

Thus the angle of the elevation is $60^{o}$

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Updated on: 10-Oct-2022

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