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suter [353]
2 years ago
13

A carousel horse travels on a circular path with a radius of 15 ft. How many feet does the horse travel over an angle of 2π3 rad

ians? Round to the nearest foot.
2π3 radians = ft
Mathematics
1 answer:
snow_lady [41]2 years ago
6 0

Answer:

arc\,\,length=10\,\pi\,ft\\arc\,\,length=31.41\,ft

Step-by-step explanation:

Recall that the formula for the length of an arc of circumference is given by the formula:

arc\,\,length=\theta\,R

where \theta is the radian form of central angle subtended , and R is the radius of the circumference. What is important is to have the angle given in radians for this formula to be valid.

In our case, the angle ( \frac{2\pi}{3} ) is already in radians, so we can apply the formula directly:

arc\,\,length=\theta\,R\\arc\,\,length=\frac{2\,\pi}{3} \,(15\,ft)\\arc\,\,length=10\,\pi\,ft\\arc\,\,length=31.41\,ft

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