To find the angle subtended by an arc of a circle, you can use the formula:
Arc Length = (θ / 360) × 2πr
where:
- θ is the angle in degrees that we want to find.
- r is the radius of the circle.
- π (Pi) is approximately 3.14159
- The arc length is 33 cm and the diameter of the circle is 28 cm.
First, find the radius of the circle. The radius is half the diameter. Therefore:
r = 28cm / 2 = 14cm
Now plug in the known values into the arc length formula:
33 = (θ / 360) × 2π × 14
To solve for θ, first calculate the denominator:
2π × 14 = 28π
So the equation becomes:
33 = (θ / 360) × 28π
Next, solve for θ by rearranging the equation:
θ = (33 × 360) / 28π
Calculate the numerical values:
θ = (11880) / (28 × 3.14159)
θ ≈ 135.00
The angle θ is approximately 135 degrees.