Find the radius of the circle if an arc of length 8 ft on the circle subtends a central angle of 225°
8/225 = 2 pi r/360 :)
To find the radius of the circle, we need to use the formula that relates the arc length, central angle, and radius of a circle.
The formula is as follows:
Arc Length = 2πr * (θ/360°)
Given:
Arc Length (l) = 8 ft
Central Angle (θ) = 225°
Rearranging the formula, we can solve for the radius (r):
r = (l * 360°) / (2π * θ)
Let's plug in the values:
r = (8 ft * 360°) / (2π * 225°)
First, simplify the equation:
r = (2880 ft * degree) / (450π degree)
The "degree" cancels out:
r = 2880 ft / (450π)
Now, we can approximate the value using a calculator:
r ≈ 2.04 ft
Therefore, the radius of the circle is approximately 2.04 feet.