Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)
Radius r: 20 feet
Central Angle θ: π/4
Arc Length s: radians
arclength = rØ
you know both r and Ø, just plug in.
To find the length of the arc, we can use the formula:
Arc Length (s) = r * θ
Given that the radius (r) is 20 feet and the central angle (θ) is π/4 radians, we can substitute these values into the formula:
Arc Length (s) = 20 * (π/4)
Now, let's calculate the value of the arc length:
Arc Length (s) = 20 * (π/4) = 5π feet
To round the answer to two decimal places, we can use the approximation 3.14 for π:
Arc Length (s) ≈ 5 * 3.14 ≈ 15.70 feet
Therefore, the length of the arc intercepted by a central angle of π/4 radians on a circle with a radius of 20 feet is approximately 15.70 feet.
To find the length of the arc on a circle of radius r intercepted by a central angle θ, you can use the formula:
Arc Length (s) = r * θ
Given:
Radius (r) = 20 feet
Central Angle (θ) = π/4 radians
Substitute these values into the formula:
Arc Length (s) = 20 * (π/4)
To calculate the value, multiply 20 by π/4:
Arc Length (s) = (20 * π)/4
Simplify:
Arc Length (s) = 5π
The length of the arc is 5π feet.