Question

From the top of a hill the angle of depression of two consecutive kilometre stones due east are found to be 45° and 30° respectively find the height of the hill

Answer 1

Answer:

1.366 km

Step-by-step 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