Question

for #16 and 17, in circle o with radius of length r, central angle poq intercepts (widehat{qp}). find the length of (widehat{qp}) in terms of (pi) for each given degree measure of (angle poq) and value of r.

1. (\theta = 175^{circ}, r = 20)
2. (\theta = 90^{circ}, r = 50)

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Substitute the values for problem 16

Given \(\theta = 175^{\circ}\) and \(r = 20\).

$$
LATEXBLOCK0
$$

Step3: Substitute the values for problem 17

Given \(\theta = 90^{\circ}\) and \(r = 50\).

$$
LATEXBLOCK1
$$

Answer:

1. \(\frac{175\pi}{9}\)
2. \(25\pi\)