Question

A survey team is trying to estimate the height of a mountain above a level plain. from one point on the plain, they observe that the angle of elevation to the top of the mountain is 28 ∘ . from a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 30 ∘ .

Answer 1

The height of the mountain is 11650 ft.

At the angle of 28 degree apply the tangent law

tan28=
`(h)/(x)` Eq.1

At the angle of 30 degree apply the tangent law

tan30=
`(h)/((x-1000))` Eq. (2)

On solving eq. (1) and Eq. (2)

The height of the mountain is h=11650 ft.