Question

The diameter of a circle is 18 feet. What is the length of a 150° arc?

Answer 1

The general working equation to find the length of the arc given the angle is

`\text{arc}=2\pi r((\theta)/(360))`

The angle given in the problem is 150 degrees. Also, the diameter of the circle is given in the problem. What we need is the radius of the circle before we proceed with the calculation of the arc length of the 150 degrees arc. The radius of the circle is just half of the diameter, hence, we have

`r=(d)/(2)=(18ft)/(2)=9ft`

We can now proceed with the calculation of the length of the arc. Just substitute the angle and the radius on the working equation and compute

`\text{arc}=2\pi(9ft)((150)/(360))=23.56\approx24ft`

Therefore, the length of the 150-degree arc is equal to 24 ft.