Question

From the top of a hill, the angles of depression of two consecutive stones due east
are found to be at 30° and 45º. Find the height of the hill.​

Answer 1

I don't know this answer please tell your class and book

Answer 2

Answer:

Let AB is the height of the hill and two stones are C and D respectively where depression is 45 degree and 30 degree. The distance between C and D is 1 km.

Here depression and hill has formed right angle triangles with the base. We have to find the height of the hill with this through trigonometry.

In triangle ABC, tan 45 = height/base = AB/BC

or, 1 = AB/BC [ As tan 45 degree = 1]

or, AB = BC ..........(i)

Again, triangle ABD, tan 30 = AB/BD

or,

$\tan(30) = \frac{ab}{bc + cd} \tan(30) =1/1.732 = \\ \frac{ab}{ab + 1} \: \: \: \: \: \: \: \: as \: given \: \: ab \: = bc$

[ As AB = BC from (i) above]

or, 1.732 AB = AB +1

or, 1.732 AB - AB = 1

or, AB(1.732-1) = 1

or, AB * 0.732 = 1

or AB = 1/0.732 = 1.366

Hence height of the hill 1.366 km