Question

a high - fountain of water is located at the center of a circular pool as shown in the figure below. not wishing to get his feet wet, a 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 55.0°. how high is the fountain? the student walks around the pool and measures its circumference to be 30.0 m. then, 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 55.0°. how high is the fountain? details my notes ask your teacher

Explanation:

Step1: Find the radius of the circular pool

We know that the formula for the circumference of a circle is $C = 2\pi r$, where $C = 30.0$ m. Solving for $r$, we get $r=\frac{C}{2\pi}=\frac{30.0}{2\pi}$ m.

Step2: Use the tangent - function to find the height of the fountain

We are given the angle of elevation $\theta = 52.0^{\circ}$. In a right - triangle formed by the radius of the pool (adjacent side) and the height of the fountain (opposite side), $\tan\theta=\frac{h}{r}$, where $h$ is the height of the fountain. So $h = r\tan\theta$. Substituting $r=\frac{30.0}{2\pi}$ and $\theta = 52.0^{\circ}$ (and $\tan(52.0^{\circ})\approx1.2799$), we have $h=\frac{30.0}{2\pi}\times1.2799$.
$h=\frac{30.0\times1.2799}{2\pi}\approx\frac{38.397}{2\pi}\approx6.11$ m

Answer:

$6.11$ m