Question

Please help me out!!!!

Answer 1

To find the length of the arc, you want to multiply the circumference of the circle by the fraction of the degrees in a full circle (360°) that the angle creating the arc PQ covers.

The angle of a complete circle is 360°. Since you are given all the angles except for the angle creating the arc PQ, you can subtract your given angles angles from 360° to get your missing angle:
360°-150°-73°-65° = 72°

The angle creating the arc PQ is 72°. That means the fraction of the full circle that the arc takes up/covers is:
`(72\°)/(360\°) = (1)/(5)`. The arc is 1/5 the entire arc/circumference of the circle.

Now find the circumference. Remember that the equation for circumference is
`c = 2 \pi r`, where c=circumference and r=radius. You're given that the radius, r = 6.48 in. Plug that into the circumference equation to find the circumference of the circle:

`c = 2 \pi r\\ c = 2 \pi (6.48 \: in)\\ c = 12.96\pi \: in`

Now multiply the fraction that the arc covers by the circumference. You know the arc is 1/5 the circumference:

`(1)/(5) * 12.96 \pi \: in \approx 8.1 \:in`

The length of the arc PQ is about 8.1 in.