In circle J with m, angle, H, J, K, equals, 94, degreesm∠HJK=94 ∘ and H, J, equals, 14HJ=14 units, find the length of arc, H, K HK⌢ . Round to the nearest hundredth.
Question
In circle J with m, angle, H, J, K, equals, 94, degreesm∠HJK=94 ∘ and H, J, equals, 14HJ=14 units, find the length of arc, H, K HK⌢ . Round to the nearest hundredth.
Solution
To find the length of arc HK, we need to use the formula for the length of an arc, which is:
Arc length = (central angle/360) * 2πr
Here, the central angle is given as 94 degrees and the radius of the circle (r) is half of the diameter, which is given as 14 units. So, r = 14/2 = 7 units.
Substituting these values into the formula, we get:
Arc length = (94/360) * 2π * 7
Now, we just need to calculate this expression to find the length of arc HK.
Arc length = 0.2611 * 2 * 3.1416 * 7 = 11.51 units
So, the length of arc HK is approximately 11.51 units, rounded to the nearest hundredth.
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