(a) an angle 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 subtends?
since s = rθ,
35/θ = 28/24
Pls and this question pls
A pie
To find out what angle an arc of length 35 cm subtends in the same circle, we can use the concept of angles subtended by arcs.
According to the given information, an angle of length 28 cm subtends an angle of 24 degrees at the center of the circle. We can use this information to establish a relationship between the length of an arc and the angle it subtends.
The formula for finding the relationship between the length of an arc and the corresponding central angle is:
Arc Length = (Central Angle / 360 degrees) * Circumference of the circle
We know the length of the first arc (28 cm) and the corresponding central angle (24 degrees). So, let's use this information to determine the circumference of the circle.
28 cm = (24 degrees / 360 degrees) * Circumference
Now we can rearrange the formula to solve for the circumference:
Circumference = (28 cm * 360 degrees) / 24 degrees
Circumference = 420 cm
Now that we know the circumference of the circle is 420 cm, we can use it to find the angle subtended by an arc of length 35 cm.
35 cm = (Central Angle / 360 degrees) * 420 cm
Rearranging the formula to solve for the central angle, we have:
Central Angle = (35 cm * 360 degrees) / 420 cm
Central Angle = 30 degrees
Therefore, an arc of length 35 cm subtends an angle of 30 degrees in the same circle.