If the measure of EF is 90° , what is the arc length of EF?

Step-by-step explanation:

We can note a couple of relationships in this circle.

The arc length will be a fraction of the circumference. It will be the same fraction of the circumference that the central angle is to the entire circle.

First step: Find the circumference of the circle.

The circumference of any circle can be defined by the formula , where r is the radius of the circle. The radius is given to us, 30 in. We can now substitute that into the formula.

So our circumference is 60π.

Second Step: Find the ratio of the central angle of the arc to the total circle degrees

We know that the total amount of degrees in a circle is 360°. Therefore, we can set up a proportion to find the ratio between the central angle (90°) and the total circle measurement.

Third Step: Equal out the two proportions and solve for the missing arc length

Now that we have our base proportion (), we can turn 60π into a proportion as well, leaving 60π as the denominator so we can solve for the arc length.

We can now solve for x by cross multiplying.

Hope this helped!

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step-by-step explanation: