Question

complete the proportion to find the arc length of the minor arc \\(\widehat{pq}\\).

what is the measure of the central angle for the minor arc, \\(\widehat{pq}\\)? \\(^{\circ}\\)

\\\frac{ }{360^{\circ}} = \frac{s}{2\pi( )}\\

find the arc length of \\(\widehat{pq}\\). write your answers using \pi\ with no spaces.

\\(\text{length}_{\text{arc}} =\\) units

Explanation:

Find the central angle of the minor arc

$$ \theta = 360^\circ - 210^\circ = 150^\circ $$

Complete the arc length proportion

$$ \frac{150^\circ}{360^\circ} = \frac{s}{2\pi(30)} $$

Calculate the arc length

$$ s = \frac{150}{360} \cdot 2\pi(30) = \frac{5}{12} \cdot 60\pi = 25\pi $$

Answer:

Question 1

What is the measure of the central angle for the minor arc, \(\widehat{PQ}\)? <blank>150</blank>\(^\circ\)

Question 2

$$\frac{\text{150}}{360^\circ} = \frac{s}{2\pi(\text{30})}$$

Question 3

\(\text{Length}_{\text{arc}} =\) <blank>25pi</blank> units