Arc Length Formula
The arc length formula is used to find the length of an arc of a circle. An arc is a part of the circumference of a circle.
Again, when working with π, if we want an exact answer, we use π. If we want to approximate an answer, we substitute a rounded form of π, such as 3.14.Also, r refers to the radius of the circle which is the distance from the center to circumference of a circle. The symbol theta, θ, is used for angle degree measures.
Example 1:
Find the arc length of an arc formed by 60° of a circle with a radius of 8 inches.
Step 1:
Find the variables.
θ = 60°
r=8
Step 2:
Substitute into formula.
Step 3:
Evaluate for Arc Length
If you want an approximate answer, use 3.14
Length =8.37
Answer:
The length is about 8.37 inches.
Example 2:
Find the arc length of an arc formed by 75° of a circle with a diameter of 18cm.
Step 1:
Find the variables.
θ = 75°
r = 9 since that is half of the diameter.
Step 2:
Substitute into formula.
Step 3:
Evaluate for Arc Length
If you want an approximate answer, use 3.14
Length = 11.78
Answer:
The length is about 11.78 inches.
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