Question

A tower of height 20 m casts a shadow of
$20 \sqrt{3} m$
Find the altitude of sun and try to give full solution.

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Answer 1

Let A be the foot of the tower. Let B be the top of the tower. Let C be the end point of the shadow. Let P be the point where Sun is. Let CAD be the horizontal line. Let DP be the line with the Sun.

Let θ be the angle made by line CBP with the horizontal CAD.

Tanθ = AB/AC = 20/(20 sqrt3) = 1/sqrt3.

θ = 30°.

We know distance of Earth from Sun.
CD = 150 × 10^6 km .

So DP = CD × Tanθ = ( 150/ sqrt3) × 10^6 km.

That will be the height above the horizon.