Question

9. Find the length of the arc shown in brown. Leave your answer in terms of . (1 point) 60° 24 ft O 4 in. O ex ft O 16 in. 0 48x in.

Answer 1

24 ft is the length of the diameter of the circle, then the measure of brown arc (in sexagesimal degrees) is 180° - 60° = 120°

180° is equivalent to π radians, then 120° is equivalent to:

$120\cdot\frac{\pi\text{ radians}}{180\text{ \degree}}=\frac{2}{3}\pi\text{ radians}$

The arc length formula is:

$s=r\cdot\theta$

where θ is the central angle (in radians), r is the radius, and s is the length of the arc.

Substituting with r = 24/2 = 12 ft and θ = 2/3 π radians, we get:

$\begin{gathered} s=12\cdot\frac{2}{3}\pi \\ s=8\pi\text{ ft} \end{gathered}$