Question

10 find the length of $overparen{knj}$.12 if $su = 37$, find the length of $overparen{sur}$.

Explanation:

Problem 10: Find the length of $\overparen{KNJ}$

Step1: Identify given values

Radius $r = 16$, central angle for $\overparen{KJ}$ is $48^\circ$.

Step2: Calculate arc $\overparen{KNJ}$ angle

$\text{Angle of } \overparen{KNJ} = 360^\circ - 48^\circ = 312^\circ$

Step3: Apply arc length formula

Arc length formula: $L = \frac{\theta}{360^\circ} \times 2\pi r$
Substitute values: $L = \frac{312^\circ}{360^\circ} \times 2\pi \times 16$
Simplify: $L = \frac{26}{30} \times 32\pi = \frac{416\pi}{15} \approx 87.17$

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Problem 12: Find the length of $\overparen{SUR}$

Step1: Identify given values

Diameter $SU = 37$, so radius $r = \frac{37}{2} = 18.5$. Central angle for $\overparen{SR}$ is $151^\circ$.

Step2: Calculate arc $\overparen{SUR}$ angle

$\text{Angle of } \overparen{SUR} = 360^\circ - 151^\circ = 209^\circ$

Step3: Apply arc length formula

Arc length formula: $L = \frac{\theta}{360^\circ} \times 2\pi r$
Substitute values: $L = \frac{209^\circ}{360^\circ} \times 2\pi \times 18.5$
Simplify: $L = \frac{209}{360} \times 37\pi = \frac{7733\pi}{360} \approx 67.53$

Answer:

1. Length of $\overparen{KNJ}$: $\frac{416\pi}{15}$ (or approximately $87.2$)
2. Length of $\overparen{SUR}$: $\frac{7733\pi}{360}$ (or approximately $67.5$)