For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?

Mathematics

1 answer:

slega [8]3 years ago

5 0

Answer: 31.43 cm

Step-by-step explanation:

The length of an arc is calculated using the formula:

$\frac{theta}{360}$ X 2 $\pi$ r

where : theta is the angle in degree

r = radius

If the angle is given in Radian , the length can be calculated using the formula:

L = r∅

Since , the angle is given in degree , we will use the first formula.

L = $\frac{theta}{360}$ X 2 $\pi$ r

L = $\frac{120}{360}$ X 2 X π X 15

L = $\frac{1}{3}$ X 2 X $\frac{22}{7}$ X 15

L = $\frac{660}{21}$

L = 31.42857143

L ≈ 31.43 cm

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<h3>What is speed?</h3>

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To find what was Beth's speed:

Beth's data:

time = 2 hrs; rate = r mph; distance = r×t = 2r miles

Tim's data:

time = 1 hr; rate = r-6 mph; distance = r-6 miles

Equation:

distance + distance = 174 miles

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2r + r - 6 = 174
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Therefore, Beth's speed was 60 mph.

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1 year ago

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