From the top of a hill, the angles of depression of two consecutive kilometer stones due to east are found to be 30° and 45°. Find the height of the hill (or) what is the height of the hill?
1 Answer
Dec 2, 2017
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,
or,
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