Question

For a circle of radius 3 feet, find the arc lengths subtended by a central angle of 57 degrees.

Answer 1

Answer: The length of an arc is 2.98 feet.

Step-by-step explanation:

Since we have given that

Radius of a circle = 3 feet

Angle subtended at the centre = 57°

We need to find the length of an arc:

As we know the formula for "Length of an arc":

$Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet$

Hence, the length of an arc is 2.98 feet.

Answer 2

$\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta = 57 \end{cases}\implies s=\cfrac{57\cdot \pi \cdot 3}{180}$