## a central angle of a circle of a radius 30cm intercepts an arc of 6cm . Express the central angle in radians and degrees ?​

Question

a central angle of a circle of a radius 30cm intercepts an arc of 6cm . Express the central angle in radians and degrees ?​

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3 months 2021-07-24T12:24:05+00:00 1 Answers 0 views 0

36/pi degrees or approximate 11.5 degrees

Step-by-step explanation:

Let’s denote the length of the intercepted arc with s, and the length of the radius r. So, s = 6 cm and r = 30 cm.                                                               When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian. To find the angle in our problem we use the following relationship:

⇒measure of an angle in radians = (length of the intercepted arc)/(length of the radius)                                                                                                   ⇒measure of our angle = s/r = 6/30 = 1/5 radians.

Now, we need to convert this measure angle in radians to degrees.

Since pi radians = 180 degrees, then 1 radians = 180/pi degrees, so:

1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.