The upper part of a tree is broken by wind and falls to the ground without being detached. if the top of the broken part touches the ground at a distance of 12 feet from the foot of the tree , calculate the height at which it is broken if the original height is 24 feet.
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Answer:
Consider
TR as the height of the tree,
TP as the broken part which touches the ground at a distance of 6m from the foot of the tree which makes an angle of 38
o
30
′
with the ground.
Take PR=x and PQ=PT=y
Thus, TR=x+y
In right triangle PQR,
tanθ=
QR
PR
Substituting the values,
⇒tan38
o
30
′
=
6
x
⇒0.7954=
6
x
⇒x=0.7954×6=4.7724
sinθ=
PQ
PR
Substituting the values,
⇒sin38
o
30
′
=
y
x
⇒0.6225=
y
4.7724
⇒y=
0.6225
4.7724
=7.6665
Hence,
Height of the tree =4.7724+7.6665=12.4389=12.44 m.
Height of the tree at which it is broken =4.77 m.
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