Question

A tower of 30 m of height stands on top of a hill. From a point some distance from the base of the hill, the angle of elevation to the top of the tower is 33°. From the same point the angle of elevation to the bottom of the tower is 32°. Find the height of the hill?

Answer 1

The height of the hill is approximately 34.52 meters.

Explanation:

Let h be the height of the hill. We can set up the following two equations using the given information:

tan 33 = (h+30)/d

tan 32 = h/d

where d is the distance from the point to the base of the hill.

We can solve for h by dividing the first equation by the second:

tan 33 / tan 32 = (h+30)/h

(h+30)/h = (tan 33)/(tan 32)

h(tan 32) + 30(tan 32) = h(tan 33)

h = 30tan 32 / (tan 33 - tan 32)

we can then use a calculator or a table of tangents to find the value of h. For example, using a calculator, we find that h = 34.52 m.

Therefore, the height of the hill is approximately 34.52 meters.