A person observes the angle of elevation of the peak of a hill from a station to be `alpha`. He walks c metres along a slope inclined at the angle `beta` and finds the angle of elevation of the peak of the hill to be `gamma`.Show that the height of the peak above the ground is `(c sinalphasin(gamma-beta))/(sin(gamma-alpha))`

Explanation

Let `A B` be the peak of a hill, so the at the station `A` the elevation of its summit is


So, `angle C AB=a^@`


Now when moving on the slope of `beta^@` by a distance of `c` `m`,


i.e., `A D` is the distance moved on the slope of `\beta^@` towards the hill,

Hence `A D= cm`

And `\angle \DAF=\beta^@`

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