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vodomira [7]
2 years ago
5

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

Mathematics
2 answers:
djyliett [7]2 years ago
6 0

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.

Leya [2.2K]2 years ago
5 0

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

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