Question

On a circle of radius 7 feet, what angle would subtend an arc of length 1 feet?

Answer 1

Answer:

The angle is 8.19 degrees.

Step-by-step explanation:

The Arc length is the measure of the distance along the curved line making up the arc.

The formula the arc measure is

                                                         $AL=2\pi r(\frac{C}{360} )$

where:

C = is the central angle of the arc in degrees

r = is the radius.

π = is Pi

From the information given we know the radius r = 7 feet and the arc of length equal to 1 feet.

So, from the above formula we solve for C.

$1=2\pi (7)(\frac{C}{360} )\\\\2\pi \left(7\right)\left(\frac{C}{360}\right)=1\\\\\frac{2\pi 7\cdot \frac{C}{360}}{14\pi }=\frac{1}{14\pi }\\\\\frac{C}{360}=\frac{1}{14\pi }\\\\C=\frac{180}{7\pi }\approx 8.19$