Question

In circle J with m HJK 144 and HJ 13 units, find the length of arc HK. Round to the nearest hundredth.

Answer 1

≈ 32.66 units

Explanation:

The measure of an arc of a circle is just part of the circumference of the circle. So we just basically use the circumference formula, but with a few tweaks:

Measure of Arch HK = (m∠HJK/360)(2
`\pi`r)

= (144/360)(2
`\pi`13)

= (0.4)(26
`\pi`)

= (10.4
`\pi`)

≈ 32.66 units

The '144/360' is saying that we're only finding part of the circumference, or just the arch of the circle. The 'r' is the radius, which in our case, is HJ (13).

Then for the last part, I multiplied 10.4 by 3.14 (As I was too lazy to use the exact value of
`\pi`) and we get an approximate answer of 32.656 units. After rounding it, we get about 32.66 units (remember, we round up by 1 when the previous digit is 5-9).

Let me know if anything was confusing and I'll be happy to elaborate :)