A circle has a radius of 3 feet and a central angle DEF that measures 60°. What is the length of the intercepted arc DF? Use 3.14 for pi and round your answer to the nearest tenth.
To find the length of the intercepted arc DF, we need to use the formula:
arc length = (angle/360) * circumference
First, let's find the circumference of the circle. The formula for the circumference of a circle is:
circumference = 2 * pi * radius
Given that the radius is 3 feet, we can substitute this value into the formula:
circumference = 2 * 3.14 * 3 = 18.84 feet
Now, let's find the length of the intercepted arc DF. We can substitute the angle measure (60°) into the formula:
arc length = (60/360) * 18.84 = 0.1667 * 18.84 = 3.14 feet
Therefore, the length of the intercepted arc DF is approximately 3.1 feet when rounded to the nearest tenth.
Wouldn't the arc length simply be 1/6 of the circumference? ( 60°/360° = 1/6 )
Circumf. = (1/6)(2π)(3) , from C = 2πr
= ....
I will let you do the arithmetic.