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°

Step-by-step 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°

$\dfrac{\pi}{180^o}=\dfrac{\pi}{5x}\\\\\\5\pi x=180^o \pi\\\\\\x=\dfrac{180^o\pi}{5\pi}\\\\\\x=36^o$