Question

Consider circle H with a 3 centimeter radius. If the length of minor arc RT is

2

3

π, what is the measure of ∠RST?

Answer 1

Answer:

$\angle RST=20^{\circ}$

$\angle RST=\frac{\pi}{9}$

Step-by-step explanation:

Please consider the attached graph of circle.

We have been given that circle H has a radius of 3 centimeters. The length of minor arc RT is $\frac{2}{3}\pi$. We are asked to find the measure of angle RST.

We will use arc length formula to find central angle.

$\text{Arc length}=r\cdot \theta$, where theta is central angle in radians.

Upon substituting our given values in arc length formula, we will get:

$r\cdot \theta=\frac{2}{3}\pi$

$3\cdot \theta=\frac{2}{3}\pi$

$\frac{3\cdot \theta}{3}=\frac{\frac{2\pi}{3}}{3}$

$\theta=\frac{2\pi}{3\cdot 3}$

$\theta=\frac{2\pi}{9}$

We know that the measure of inscribed angle is half the measure of central angle.

$\angle RST=\frac{1}{2}\angle RHT$

$\angle RST=\frac{1}{2}\cdot \frac{2\pi}{9}$

$\angle RST=\frac{\pi}{9}$

The measure of angle RST is in radians, we will convert it in degrees as:

$\angle RST=\frac{\pi}{9}\times \frac{180^{\circ}}{\pi}$

$\angle RST=20^{\circ}$

Therefore, measure of angle is $\frac{\pi}{9}$ in radians or 20 degrees.

Answer 2

Answer:

20 degrees

Step-by-step explanation:

s = 2πr x  

n°

360°

n° =  

360s

2πr

=  

360(

2π

3

)

2π(3)

= 40

thus, ∠H = 40°

then,

∠RST =  

1

2

∠H =  

1

2

40 = 20