Question

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. ​

Answer 1

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