Find the length of the arc on a circle of radius 10 ft intercepted by a central angle 276. Answer in units of ft.
C = pi*D = 3.14(2*10) = 62.8 ft = cir-
cumference.
Arc = (276/360) * 62.8 = 48.1 ft.
To find the length of the arc intercepted by a central angle, we can use the formula:
Arc Length = (Central Angle / 360 degrees) * 2 * π * Radius
Given that the radius of the circle is 10 ft and the central angle is 276 degrees, we can substitute the values into the formula.
Arc Length = (276 / 360) * 2 * π * 10 ft
Simplifying this equation, we get:
Arc Length = (0.7667) * (2 * 3.1416) * 10 ft
Arc Length ≈ 4.8089 * 10 ft
Therefore, the length of the arc intercepted by a central angle of 276 degrees on a circle with a radius of 10 ft is approximately 48.089 ft.
To find the length of the arc on a circle, you need to use the formula:
Arc length = (θ / 360) * (2π * r),
Where:
- Arc length is the length of the arc on the circle.
- θ is the measure of the central angle in degrees.
- r is the radius of the circle.
In this case, the radius of the circle is given as 10 ft, and the central angle is given as 276.
Substituting the values into the formula, we have:
Arc length = (276 / 360) * (2π * 10).
Now, we can calculate the length of the arc:
Arc length = (276 / 360) * (2 * 3.14159 * 10).
Simplifying the expression:
Arc length = (69 / 90) * (62.8318).
Calculating the result:
Arc length ≈ 47.7489 ft.
Therefore, the length of the arc intercepted by a central angle of 276 degrees on a circle with a radius of 10 ft is approximately 47.7489 ft.