Question

From top of the hill the angle of depressiob of two consecutive kilometer stones due east are found to be 45° and 30° respectively. Find the height of the tower

Answer 1

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