The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\...

Answer Details

To find the radius of the circle, we need to use the formula: $$ \text{length of arc} = \theta \frac{\pi r}{180} $$ where $\theta$ is the angle subtended by the arc at the center of the circle, $r$ is the radius of the circle, and $\pi$ is the mathematical constant pi. Substituting the given values, we get: $$ 50 = 75 \times \frac{\pi r}{180} $$ Simplifying the equation, we get: $$ r = \frac{50 \times 180}{75 \times \pi} \approx 38.2 \text{ cm (to 3 significant figures)} $$ Therefore, the correct answer is 38.2cm.