Enter the base length and angle at the circumference into the calculator to determine the arc length according to Thales’ theorem. This calculator can also evaluate any of the variables given the others are known.
Thales Theorem Formula
The following formula is used to calculate the arc length based on Thales’ theorem.
L = (theta / 360) * (pi * B)
Variables:
- L is the arc length (units)
- (theta) is the angle at the circumference (degrees)
- B is the base length of the circle (units)
To calculate the arc length, multiply the angle at the circumference by the base length of the circle and then divide by 360 degrees. Multiply this result by (pi) to get the arc length.
What is Thales Theorem?
Thales’ theorem states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle (90 degrees). This theorem can also be used to calculate the arc length of a circle based on the angle subtended at the center of the circle by that arc.
How to Calculate Arc Length using Thales Theorem?
The following steps outline how to calculate the arc length using Thales’ theorem.
- First, determine the base length of the circle (B) in units.
- Next, determine the angle at the circumference ((theta)) in degrees.
- Next, gather the formula from above = L = ((theta) / 360) * ((pi) * B).
- Finally, calculate the arc length (L) in units.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Base length of the circle (B) = 10 units
Angle at the circumference ((theta)) = 60 degrees
