Question

a central Angle of a circle of radius 50cm intercept an arc of 10cm. express the central Angle in radian an degrees​

Answer 1

Answer: π/5 = 36°

Explanation:

The formula for the arc length of a circle is: s = r Ф (Ф must be in radians)

Given: s = 10, r = 50

s = r Ф

10 = 50 Ф

(1/5)π = Ф (We include π because it must be in radians)

Convert into degrees using the proportion π = 180°

`(\pi)/(180^o)=(\pi)/(5x)\\\\\\5\pi x=180^o \pi\\\\\\x=(180^o\pi)/(5\pi)\\\\\\x=36^o`