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A tree of 15 m height is broken by the wind so that its top touches the ground and makes an angle of 30° with the ground. Find the length of the broken part of the tree. ​

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Answer:

10 m

Explanation:

the situation can be modelled by a right triangle with hypotenuse the broken branch and opposite side to 30° being the remaining tree.

let x be the length of the broken branch, then remaining part of the tree is 15 - x

using the sine ratio in the right triangle and the exact value

sin30° =
(1)/(2) , then

sin30° =
(opposite)/(hypotenuse) =
(15-x)/(x) =
(1)/(2) ( cross- multiply )

x = 2(15 - x)

x = 30 - 2x ( add 2x to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

the broken part of the tree is 10 m

User Ankit Dubariya
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