Find the angle subtended by an arc 33cm long of a circle of diameter 28cm.

Answer Details

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.