Question

Determine length of an arc included in an angle.of 45°.when the diameter of the circle is 6 inches

Answer 1

Hello!

As the diameter is 6, we know the radius is 3. To convert degrees to radians, we use the following formula. We will have pi=3.14.


`x( ( \pi )/(180))`

We will plug in our x value.

45(
`\pi`)/180

`(45 \pi )/(180) = ( \pi )/(4)`

Therefore, our arc length is pi/4 radians. This is about 0.79. If we multiply this by our radius, 3, we get an arc length of about 2.37 inches.

I hope this helps!

Answer 2

The appropriate formula is
s = r·θ
where s is the arc length, r is the radius, and θ is the central angle in radians.

You have r = (6 in)/2 = 3 in, and θ = 45° = π/4 radians. Then
s = (3 in)·(π/4) = 3π/4 in ≈ 2.356 in