Question

A high fountain of water is located at the center of a circular pool. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55°. How high is the fountain?

Answer 1

The fountain is 3.43 m high.

Step-by-step explanation:

Circumference of the pool = 15 m.

C = 2
`\pi`r

where C is the circumference and r its radius.

r =
`(C)/(2\pi )`

=
`(15)/(2((22)/(7)) )`

r = 2.3864

radius of the pool = 2.40 m

So that the height of the fountain, h, can be determined by applying trigonometric function.

Tan θ =
`(opposite)/(adjacent)`

Tan 55 =
`(h)/(2.4)`

h = Tan 55 x 2.4

= 1.4282 x 2.4

= 3.4277

h = 3.43 m

The height of the fountain is 3.43 m.