Question

find the radius of the circle in which a central angle of 60° intercepts an arc of length 37.4 cm.

Answer 1

$given \: \\ l = 37.4cm$
angle=60°

$radian \: measure = \frac{\pi}{180} \times degree \: measure \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi}{180} \times 60 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi}{3}$
$radius = \frac{arc}{radian} \\ r = \: \: \frac{37.4}{ \frac{\pi}{3} } \\ r = \: \: \frac{37.4 \times 3}{\pi} \\ r = 35.7cm$

Answer 2

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Given,

Length of the arc = l = 37.4 cm

Central angle = θ = 60° = 60π/180 radian = π/3 radians

We know that,

r = l/θ

= (37.4) * (π / 3)

= (37.4) / [22 / 7 * 3]

= 35.7 cm

Hence, the radius of the circle is 35.7 cm

Hope it's Helpful....:)