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# 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 and in radians. θ = degrees (Round your

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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 and in radians. θ = degrees (Round your answer to one decimal place.) θ = radians

Guest Jan 19, 2016

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Circumference = 2pi*r = 2pi*4 = 8pi

so

$$\frac{5}{8\pi}=\frac{\theta\;radians}{2\pi}\\ \frac{5*2\pi}{8\pi}=\theta\;radians\\ \theta=\frac{5}{4}\;radians\\~\\ now\\ \pi radians=180 degrees\\ so\\ 1 radian = \frac{180}{\pi}degrees\\ \frac{5}{4}\;radians=\frac{5}{4}*\frac{180}{\pi}degrees\\ \frac{5}{4}\;radians=\frac{225}{\pi}degrees\\~\\ \theta\approx 71.6 \;degrees$$

Melody  Jan 21, 2016
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#1
+91051
+10

Circumference = 2pi*r = 2pi*4 = 8pi

so

$$\frac{5}{8\pi}=\frac{\theta\;radians}{2\pi}\\ \frac{5*2\pi}{8\pi}=\theta\;radians\\ \theta=\frac{5}{4}\;radians\\~\\ now\\ \pi radians=180 degrees\\ so\\ 1 radian = \frac{180}{\pi}degrees\\ \frac{5}{4}\;radians=\frac{5}{4}*\frac{180}{\pi}degrees\\ \frac{5}{4}\;radians=\frac{225}{\pi}degrees\\~\\ \theta\approx 71.6 \;degrees$$

Melody  Jan 21, 2016
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An arc of length 75 m subtends a central angle θ in a circle of radius 25 m. Find the measure of θ in degrees and in radians.

Guest Jun 17, 2016

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