Q1 of 47 Page 1

The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

The figure is given below:


Let AB be the height of the tower = x m


Let BC be the length of the shadow = y m


Let θ be the angle of elevation.


Given that the ratio of the height of the tower and length of the shadow is √3 : 1.


∴ x:y = √3:1


⇒ x/y = √3/1 ……… (1)


In right angled triangle ABC,


tan θ = AB/BC


⇒ tan θ = x/y


⇒ tan θ = √3 (from equation (1))


⇒ tan θ = tan 60°


⇒ θ = 60°


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