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.

Explanation

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`