Question

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

Answer 1

The angle is 8.19 degrees.

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((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)((C)/(360) )\\\\2\pi \left(7\right)\left((C)/(360)\right)=1\\\\(2\pi 7\cdot (C)/(360))/(14\pi )=(1)/(14\pi )\\\\(C)/(360)=(1)/(14\pi )\\\\C=(180)/(7\pi )\approx 8.19`