Question

At a point 65 feet from the base of a church, the angles of elevation to the bottom of the steeple and the top of the steeple are 35° and 43°, respectively. Find the height of the steeple.​

Answer 1

15.10 ft to nearest hundredth.

Explanation:

We have 2 right triangles one within the other

For the larger triangle

tan 43 = h / 65 where h is the total height to the top of steeple from ground

h = 65 tan 43

For small triangle

tan 35 = h2 / 65 where h2 is the hoght of the bottom of steeple from the ground

h2 = 65 tan 35

So height of the steeple

= h - h2

= 65 tan43 - 65 tan35

= 15.099 feet.