Answer:
The angle subtended at the centre O by the arc of length 19 cm and radius 30 cm is 36.27°.
Explanation:
The radius of the circle, r = 30 cm
The length of the arc of the circle, l = 19 cm
The formula for the arc length of a circle is given by,
l = 2πr * [θ/360°] ……. [Here θ = angle subtended at the centre O by the arc]
Now, substituting the given values in the above formula, we get
19 = 2 * (22/7) * 30 * [θ/360°]
⇒ 19 = 188.57 * [θ/360°]
⇒ θ = [360 * 19] / [188.57]
⇒ θ = 36.27°
Thus, the angle subtended by the arc at the centre O is 36.27°.