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Some portion of a 20 meters long tree i...

Some portion of a 20 meters long tree is broken by the wind and its top struck the ground at an angle of `30 ^@`.Find the height of the point where the tree is broken.

Text Solution

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Let AD be the tree before it was broken . AD= 20 m
Tree is broken at point B and the broken portion is touching the ground at point C. In triangle BAC,

`sin 30^@ =(h)/(20 -h )`
`rArr 1/2= (h)/(20 -h)`
`rArr 20 -h = 2h `
`rArr h=(20)/(3) m`
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