From the top of the hill , the angles of depression of two consecutive kilometer stones due east are found to be 30 and 45 degrees, find the height of the hill

The height of hill is 1.366 km

Solution:

The figure is attached below

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

CD = 1 km

Here depression and hill has formed right angle triangles with the base

To find: height of hill

height of hill = AB

In triangle ABC,

We know tan 45 (in degrees) = 1

AB = BC ----- eqn 1

In triangle ABD,

From attached figure, BD = BC + CD

Also we know that,

As AB = BC from eqn 1 and CD = 1 km,

Hence the height of hill is 1.366 km

range is infinite on both x and y axis positive and negative

step-by-step explanation: