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A tree stands vertically on a hill side ...

A tree stands vertically on a hill side which makes an angle of `15^0` with the horizontal. From a point on the ground 35 m down the hill from the base of three, the angle of elevation of the top of the tree is `60^0` . Find the height of the tree.

Text Solution

Verified by Experts

Let `PQ` be tree an d`A` be the point on ground `AR` such that `AP=35m`
Now `< QAR=60^@` and `< PAR=15^@`
`< PAQ= < QAR - < PAR=60^@-15^@=45^@`
`< AQP=90^@ - < QAR=90^@-60^@=30^@`
Using sine rule,
`frac{AP}{sin 30^@}=frac{PQ}{sin 45^@}`
`=>frac{35}{frac{1}{2}}=frac{PQ}{frac{1}{sqrt(2)}}`
`PQ=35sqrt(2)m`
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Knowledge Check

  • A vertical pole stands on the level ground. From a point on the ground, 25m away from the foot of the pole , the angle of elevation of its top is found to be 60^(@) . Find the height of the pole.

    A
    `25sqrt(3)`
    B
    `50sqrt(3)`
    C
    `55sqrt(3)`
    D
    `65sqrt(3)`

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