At the foot of a mountain the elevation of its summit is `45^@`, after ascending 1000m towards the mountain up a slope of `30^@` inclination, the elevation is found to be `60^@` Find the height of the mountain.

Explanation

Let {F} be the foot and {S} be the summit of the mountain F O S
.
Then, angle O F S`=45^{circ}` and therefore` angle O S F=45^{circ}`.

O F=O S=h {km} (say)

Let F P=1000 {m}=1 {km} be the slope so that

angle O F P`=30^{circ}.` Draw PM perp O S and PL perp O F.

Join PS. It is given that angle {MPS}`=60^{circ}.`

In Delta {FPL}, We have

`sin 30^{circ}=frac{P L}{P F}`