To calculate the length of the arc of a circle given the radius and the angle of the arc in degrees, you can use the formula:
Arc length = (angle / 360) * Circumference of the circle
The circumference of the entire circle is given by the formula:
Circumference = 2 * π * radius
You are given that the radius (r) is 66, and the angle (T) subtended by the arc is 90°.
Let's calculate the circumference first:
Circumference = 2 * π * r
Circumference = 2 * π * 66
Now, let's use the first formula to calculate the arc length, using the given angle of 90 degrees:
Arc length = (T / 360) * Circumference
Arc length = (90 / 360) * (2 * π * 66)
Since 90/360 simplifies to 1/4, the formula becomes:
Arc length = (1/4) * (2 * π * 66)
Now simplify the constant factors:
Arc length = 1/2 * π * 66
To express this in terms of T, we would write:
Arc length = (T / 360) * (2 * π * 66)
But as T is given to be 90 degrees, we can calculate the numerical value as:
Arc length ≈ 103.67
Note that in the final step of the calculation, we substituted the value of π with its numerical approximation and rounded the result to the hundredths place, which gives us approximately 103.67 as the length of the arc.
