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A portion of 60 m long tree is broken by tornado and the top struck up the ground making an angle of $300$ with the ground level. Find the height of the point where the tree is broken.

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5 m

20 m

15 m

10 m

answer is D.

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Detailed Solution

Given that the tree is 60m long. Suppose the height of the point where the tree is broken is x. Then the length of the broken part is

60 − x

.
We have to find the value of height.
Question Image

In a right-angle triangle,

sin θ = Opposite side Hypotenuse

From the right-angle triangle BCD,

sin 30 ° = B C C D ⇒ 12 = x 60 − x ⇒ 60 − x = 2 x ⇒ 3 x = 60 ⇒ x = 20 m

The height of the point where the tree is broken is 20m.
Therefore, the correct option is 4.

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