how to you solve: the radius of circle Z is 13.5 units long. Find the length of each arc for the given angle measure. if the angle measure is 120 degrees?
he radius of
Z is 13.5 units long. Find the length of each arc for the given angle measure.
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To find the length of an arc in a circle, you can use the formula:
Arc Length = (Angle Measure / 360) x (2πr)
where:
- "Angle Measure" is the measure of the angle in degrees,
- "r" is the radius of the circle, and
- "π" (pi) is a mathematical constant approximately equal to 3.14.
In this case, the radius of circle Z is given as 13.5 units, and the angle measure is 120 degrees. Therefore, we can substitute these values into the formula to calculate the length of the arc.
Arc Length = (120/360) x (2 x 3.14 x 13.5)
Let's solve this equation step by step:
Step 1: Simplify the fraction (120/360) by dividing both the numerator and denominator by their greatest common divisor, which is 120:
120 ÷ 120 = 1
360 ÷ 120 = 3
So now the equation becomes:
Arc Length = (1/3) x (2 x 3.14 x 13.5)
Step 2: Evaluate the expression within the brackets:
(2 x 3.14 x 13.5) = 84.78
Now the equation becomes:
Arc Length = (1/3) x 84.78
Step 3: Simplify the remaining fraction (1/3) by dividing the numerator by the denominator:
1 ÷ 3 ≈ 0.33 (rounded to two decimal places)
Now the equation becomes:
Arc Length ≈ 0.33 x 84.78
Step 4: Evaluate the product of the two values:
(0.33 x 84.78) ≈ 28.02
Therefore, the length of the arc for an angle measure of 120 degrees in circle Z with a radius of 13.5 units is approximately 28.02 units.