Jessica is building a round pen for her horse. She has picked out a pen with a 50-foot radius.

Her father told her that if he would pay for the fencing that creates a 270-degree arc and that she will have to earn the rest. How many feet of fencing will Jessica have to pay for?

Fill in the following blanks. Use the variable x or y for unknown values. Move your mouse over the blanks to reveal the answers.

• To find the feet of fencing Jessica is paying for the ______ arc length is found.
• The circular area has a radius of 50 feet; the circumference is __________. 2(50) = 100 = 314 feet.
• Jessica's father will pay for 270° of fencing and Jessica will pay for ______ 360 – 270 = 90 degrees of fencing.
• The ratio of the degree measure of the sector to the degree measure of the circle is ______. 90 360
• The proportion is _____________________. Degree measure of sector Degree measure of circle = Arc length Circumference = 90 360 = x 314 OR 1 4 = x 314
• Find the cross product. ______. 1(314) = 4(x)
• The arc length is ______________________. 1(314) = 4(x) ⇒ 314 ÷ 4 = x ⇒ x = 78.6 ft

Close this window/tab to return to the lesson.