Question

From the top of the hill, the angle of depression of two roadways stones with one kilometer distance are found Tobe 30 and 60 .find the height of the hill

Answer 1

Hope it helps!

Answer is given in image

Answer 2

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,

1

√

3

=

A

B

B

C

+

C

D

[tan 30 =

1

√

3

=1/1.732]

or,

1

1.732

=

A

B

A

B

+

1

[ 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