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5 A circle has a radius of 12 in. Find an exact value for each measurement. (Hint: Use arc length formula to find angle)
a) an arc length with a central angle of 90°:
b) the area of a sector with a central angle of 90°:​

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MrRoyal

Answer:

[tex](a)\ L = 18.84[/tex] --- arc length

[tex](b)\ A = 113.04[/tex] --- sector area

Step-by-step explanation:

Given

[tex]r = 12[/tex]

[tex]\theta = 90[/tex]

Solving (a): The arc length

This is calculated using:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

So, we have:

[tex]L = \frac{90}{360} * 2* 3.14 * 12[/tex]

[tex]L = 0.25* 2* 3.14 * 12[/tex]

[tex]L = 18.84[/tex]

Solving (b): The sector area

This is calculated using:

[tex]A = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]A = \frac{90}{360} * 3.14 * 12^2[/tex]

[tex]A = 0.25 * 3.14 * 12^2[/tex]

[tex]A = 113.04[/tex]

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