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Talja [164]
3 years ago
12

A central angle θ in a circle of radius 4 m is subtended by an arc of length 5 m. find the measure of θ in degrees. (round your

answer to one decimal place.)
Mathematics
1 answer:
koban [17]3 years ago
5 0

Answer:

\theta=71.6\°

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

C=2\pi r

we have

r=4\ m

substitute the values

C=2\pi (4)=8 \pi\ m

step 2

Remember that

360 degrees subtends the arc of length  8 \pi\ m (circumference)

so

by proportion

Find the measure of θ by an arc of length 5 m

assume \pi=3.1416

\frac{360}{8\pi}=\frac{\theta}{5}\\ \\ \theta=360*5/8\pi \\ \\ \theta=71.6\°

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