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A circle with radius 4 inches has a central angle of 45 degrees. What is the length of the inscribed arc? Round to the nearest tenth, if necessary. [Hint: convert the angle measure to radians.] Best answer gets Brainliest!!

a. 1.57 inches
b. 3.14 inches
c. 4.19 inches
d. 6.28 inches

Respuesta :

3.14 inches is the length of the inscribed arc

The length of the inscribed arc is given by option b. 3.14 inches.

What is arc length of a circle?

"The length of the inscribed arc of a circle is the distance between two points along a section of a curve."

What is central angle of a circle?

"The central angle of a circle is the angle between two radii of a circle."

Formula to calculate the length of the inscribed arc:

[tex]s=r[/tex] × [tex]\theta[/tex]

where [tex]s[/tex] represents  the length of the inscribed arc

[tex]r[/tex] is the radius of the circle

[tex]\theta[/tex] represents the central angle of a circle in radians

Formula to convert angle in degrees to radians:

Ф = ∅ × (π/180)

where, ∅ is the angle measured in degrees

Ф is the angle measured in radians.

From given data,

[tex]r=4[/tex] inches

[tex]\theta=45[/tex]

So, the central angle in radians is:

⇒ [tex]\theta=45[/tex] × [tex]\frac{\pi}{180}[/tex]

⇒ [tex]\theta=\frac{\pi}{4}[/tex]

And the length of the inscribed arc is: [tex]s=r[/tex] × [tex]\theta[/tex]

⇒ [tex]s=4[/tex] × [tex]\frac{\pi}{4}[/tex]

⇒ [tex]s=\pi[/tex]

⇒ [tex]s=3.14[/tex] inches

So, the length of the inscribed arc is 3.14 inches.

Hence, the correct answer is option b. 3.14 inches.

Learn more about the length of the inscribed arc here:

https://brainly.com/question/23856295

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