A 2(pi) cm wire is stretched along a circle of radius 4cm. The degree measure of the central angle subtended by this wire arc is what?
circumference = 2 pi r = 8 pi
fraction of circumference = 2 pi/8 pi = 1/4
1/4 * 360 = 90 degrees
A chord of a circle is 15 cm long and subtends at an angle of 110° at the center of the circle. Find the radius of the circle correct to 2 decimal point.
To find the degree measure of the central angle subtended by the wire arc, you can use the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius.
Given that the radius of the circle is 4 cm and the wire is stretched along the circumference, the length of the wire is equal to the circumference of the circle. Thus, we can rewrite the formula as:
2πr = length of the wire
2π(4) = length of the wire
8π = length of the wire
Now, we need to find the angle in degrees formed by an arc of length 8π cm along the circumference of the circle. Recall that the circumference of a full circle is equal to 360 degrees.
To find the degree measure of the central angle subtended by the wire arc, we need to find the ratio of the length of the wire arc to the circumference of the entire circle and multiply it by 360 degrees.
Angle in degrees = (length of the wire arc / circumference of the circle) * 360
Substituting the values we found earlier:
Angle in degrees = (8π / 8π) * 360
Angle in degrees = 360 degrees
Therefore, the degree measure of the central angle subtended by the wire arc is 360 degrees.