Question

77In a circle, an angle measuring radians intercepts an arc of length 21. Find theradius of the circle in simplest form.

Answer 1

radius = 9

Explanation

The relation between the central angle, θ (measured in radians), the arc length, and the radius, r, of a circle is shown in the next picture:

Substituting θ = 7π/6, and arc length = 21π/2, and solving for the radius:

`\begin{gathered} (21\pi)/(2)=(7\pi)/(6)r \\ (21\pi)/(2)\cdot(6)/(7\pi)=(7\pi)/(6)r\cdot(6)/(7\pi) \\ 9=r \end{gathered}`