Recall that the ratio of the length of an arc to the circumference of the circle is equal to the ratio of the degree measure of the arc to 360.
A
a
mADC=240
B
b
≈ 30.4 inches
a
We are given that a movie reel has a diameter of 14.5 inches, and we want to find mADC. Let's look at the given diagram.
From the graph we can see ADC is a major arc. Since an arc measure is related to the measure of the corresponding central angle, the measure of ADC is 240.
b
In this part we want to find the length of ADC. First, let's recall that the ratio of the length of an arc l to the circumference of the circle is equal to the ratio of the degree measure of the arc x to 360.
l/π d=x/360
Since we are given that the diameter of the circle is 14.5 inches and the measure of ADC is 240, we will substitute these values into the proportion and solve for l.
