If I had a metal circle and the circumference of that measured 6.750 inches long, how long would 38 degrees of that circle be in inches.
To determine how long 38 degrees of a circle with a given circumference would be, we can use the formula for calculating the circumference of a circle.
The formula for the circumference of a circle is: C = 2πr, where C represents the circumference and r represents the radius of the circle.
To find the radius, we can divide the circumference (6.750 inches) by 2π (approximately 6.28318).
Radius (r) = Circumference (C) / (2π)
r = 6.750 / 6.28318
r ≈ 1.0736 inches
Now that we have the radius, we can calculate the length of an arc corresponding to an angle of 38 degrees using the formula l = rθ, where l represents the length of the arc and θ represents the angle (in radians).
In order to use the formula, we need to convert the angle from degrees to radians since the formula uses radians.
To convert degrees to radians, we can use the following formula: θ (radians) = θ (degrees) * (π / 180).
θ (radians) = 38 * (π / 180)
θ (radians) ≈ 0.6632251 radians
Now we can calculate the length of the arc. Plug in the values into the formula:
Length of the arc (l) = Radius (r) * Angle (θ)
l = 1.0736 * 0.6632251
l ≈ 0.71 inches (rounded to two decimal places)
Therefore, 38 degrees of the given circle would be approximately 0.71 inches long.