Question

from the top of a hill the angles of depression of two consecutive kilometre stones due east or found to be 30 degree and 45 degree respectively find the distance of two stones from the foot of the hill

Answer 1

Answer:

1.366 km

Explanation:

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

please follow me ..

mark me as a brilliant

thanks my answer..also

thanks