Q. 245.0( 1 Vote )

# If the elevation of the sun changes from 30° to 60° then the difference between the lengths of shadows of a pole 15 m high, is

A. 7.5 m

B. 15 m

C. 10√3 m

D. 5√3 m

Answer :

Let AB be the pole and BD, BC is its shadows when the angle of elevation of the sun is 30°, 60° respectively. Here, the height of the pole is 15 m. So, AB = 15m. Join C and D with A. So we get two right-angled triangles ABC and ABD with right angle at B. And ∠ADB = 30° and ∠ACB = 60°. We are to find the difference between the length of the shadows, that is, CD. For this, we find the lengths BD and BC from triangles ABD and ABC respectively using the trigonometric ratio tan. In ∆ABC,

or,

In ∆ABD,

or,

CD = 15√3 -5√3 = 10 √3 m.

So, the correct option is (C).

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