Question

the height of a right circular cone is 15.4 centimeters, and the diameter of the base is 17.2 centimeters. see the following figure (not drawn to scale). what angle does the side of the cone make with the base (rounded to at least the nearest tenth)?

Explanation:

Step1: Find the radius of the base

The radius $r$ is half of the diameter. Given diameter $d = 17.2$ cm, so $r=\frac{d}{2}=\frac{17.2}{2}=8.6$ cm.

Step2: Use the tangent - function

Let $\theta$ be the angle the side of the cone makes with the base. In the right - triangle formed by the height, radius, and the side of the cone, $\tan\theta=\frac{h}{r}$, where $h = 15.4$ cm and $r = 8.6$ cm. So $\tan\theta=\frac{15.4}{8.6}\approx1.7907$.

Step3: Find the angle

We know that $\theta=\arctan(1.7907)$. Using a calculator, $\theta\approx60.8^{\circ}$.

Answer:

$60.8^{\circ}$