In circle K with m, angle, J, K, L, equals, 78, degreesm∠JKL=78 ∘ and J, K, equals, 6JK=6 units, find the length of arc, J, L JL⌢ . Round to the nearest hundredth.
Question
In circle K with m, angle, J, K, L, equals, 78, degreesm∠JKL=78 ∘ and J, K, equals, 6JK=6 units, find the length of arc, J, L JL⌢ . Round to the nearest hundredth.
Solution
To find the length of arc JL, we need to use the formula for the length of an arc in a circle, which is:
Arc length = (central angle/360) * 2πr
Here, the central angle is given as 78 degrees and the radius (r) is given as 6 units.
So, substituting these values into the formula, we get:
Arc length = (78/360) * 2π * 6
Now, we just need to calculate this expression to find the length of arc JL.
First, divide 78 by 360 to get approximately 0.2167.
Then, multiply this by 2π (approximately 6.2832) to get approximately 1.3611.
Finally, multiply this by 6 to get approximately 8.1666.
So, the length of arc JL is approximately 8.17 units (rounded to the nearest hundredth).
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