Questions: Find the length of an arc if the radius of the arc is 4 ft and the measure of the arc is (8 π/7) (Round answer to the nearest thousandth)
Transcript text: Find the length of an arc if the radius of the arc is 4 ft and the measure of the $\operatorname{arc}$ is $\frac{8 \pi}{7}$
(Round answer to the nearest thousandth)
Solution
Solution Steps
Step 1: Given Values
We are given the radius r=4 ft and the angle θ=78π radians.
Step 2: Arc Length Formula
The formula for the length of an arc is given by:
Arc Length=r×θ
Step 3: Substitute Values
Substituting the given values into the formula:
Arc Length=4×78π
Step 4: Calculate Arc Length
Calculating the arc length:
Arc Length=732π
Step 5: Approximate Value
To find the approximate value, we calculate:
Arc Length≈14.361566416410483
Step 6: Round to Nearest Thousandth
Rounding the arc length to the nearest thousandth gives:
Arc Length≈14.362