Consider a circle with a 9 centimeter radius and an arc subtended by an angle measuring 70°.If the subtended angle is changed from 70° to 10°, what will be the length of its corresponding arc?
To find the length of the arc, we need to use the formula:
Arc length = (angle/360) x 2πr
where:
- angle is the measure of the subtended angle in degrees
- r is the radius of the circle
Given:
- radius (r) = 9 cm
- initial angle = 70°
- new angle = 10°
Initial arc length = (70/360) x 2π x 9
Initial arc length = (7/36) x 18π
Initial arc length = 3.5π cm
For the new angle of 10°:
New arc length = (10/360) x 2π x 9
New arc length = (1/36) x 18π
New arc length = 0.5π cm
Therefore, the length of the corresponding arc when the subtended angle is changed from 70° to 10° is 0.5π cm.