Answer:
TR as the height of the tree,
TP as the broken part which touches the ground at a distance of 6 m from the foot of the tree which makes an angle of 38∘30′ with the ground.
Take PR=x and PQ=PT=y
Thus, TR=x+y
In right triangle PQR,
tanθ=QRPR
Substituting the values,
⇒tan38∘30′=6x
⇒0.7954=6x
⇒x=0.7954×6=4.7724
sinθ=PQPR
⇒sin38∘30′=yx
⇒0.6225=y4.7724
⇒y=0.62254.7724=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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Verified answer
Answer:
TR as the height of the tree,
TP as the broken part which touches the ground at a distance of 6 m from the foot of the tree which makes an angle of 38∘30′ with the ground.
Take PR=x and PQ=PT=y
Thus, TR=x+y
In right triangle PQR,
tanθ=QRPR
Substituting the values,
⇒tan38∘30′=6x
⇒0.7954=6x
⇒x=0.7954×6=4.7724
sinθ=PQPR
Substituting the values,
⇒sin38∘30′=yx
⇒0.6225=y4.7724
⇒y=0.62254.7724=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.