How to Calculate Arc Length for a 124° Angle in a Circle?

[zolton5971]

A circle has a radius of 10cm. Find the length s of the arc intercepted by a central angle of 124°
.

Do not round any intermediate computations, and round your answer to the nearest tenth.

How do I do this?

 

[MarkFL]

You will need the formula:

[box=green]

Arc Length of Circular Arc​

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The arc-length $s$ of the circular arc, where the radius of curvature is $r$, and the subtended angle is $\theta$ (in radians) is given by:

\(\displaystyle s=r\theta\tag{1}\)[/box]

So, you need to convert the given angle to radians (multiply by \(\displaystyle \frac{\pi}{180^{\circ}}\)), and then plug the given data into (1). What do you find?

 

[zolton5971]

Got that one thanks!

 

[MarkFL]

Got that one thanks!

The function f is defined by f(x)=x^2+5

Find f(3z)

How do I find f(3z)

You should have found:

\(\displaystyle s=\frac{62\pi}{9}\)

I am going to move your next question to a new thread. :D

 

[CellCoree]

To find the length of the arc intercepted by a central angle of 124°, we can use the formula for arc length: s = rθ, where r is the radius of the circle and θ is the central angle in radians.

First, we need to convert the central angle of 124° to radians by multiplying it by π/180. This gives us θ = 124° * π/180 = 2.16 radians.

Next, we plug in the given radius of 10cm into the formula:

s = (10cm) * (2.16 radians) = 21.6cm

Therefore, the length of the arc intercepted by a central angle of 124° in a circle with a radius of 10cm is approximately 21.6cm.