Chapter 6.1, Problem 58E

To determine

To calculate; radius of circle having arc $3ft$ subtends a angle of ${25}^{\circ }$ at centre.

Answer to Problem 58E

Radius $=\frac{108}{5\pi }ft\approx 67.9ft$

Explanation of Solution

Change degree to radians and use equation $S=r\theta$ .

  $\begin{array}{l}{25}^{\circ }\times \frac{\pi }{{180}^{\circ }}=\frac{{25}^{\circ }\pi }{{180}^{\circ }}=\frac{5\pi }{36}\\ (3ft)=r(\frac{5\pi }{36})\\ r=3\times \frac{36}{5\pi }=\frac{108}{5\pi }\approx 67.9ft\end{array}$