An arc of length 28cm subtends an angle of 24 at the centre of a circle in the same circle. what angle does an arc of length 35cm subtend?
We can use the formula for the relationship between the central angle, the arc length, and the circumference of a circle:
angle = (arc length / circumference) x 360 degrees
Let C be the circumference of the circle. Then we have:
24 degrees = (28 cm / C) x 360 degrees
Solving for C, we get:
C = (28 cm / 24 degrees) x (360 degrees / 1) = 420 cm
Now we can use the same formula to find the angle for an arc of length 35 cm:
angle = (35 cm / 420 cm) x 360 degrees = 30 degrees
Therefore, an arc of length 35 cm subtends an angle of 30 degrees at the centre of the circle.