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In a circle with a diameter of 25.2 ft, an arc is intercepted by a central angle of 168º.

What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

Respuesta :

calculista

Answer:

[tex]36.93\ ft[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

[tex]C=\pi D[/tex]

we have

[tex]D=25.2\ ft[/tex]

substitute

[tex]C=25.2\pi\ ft[/tex]

step 2

we know that

The circumference of a circle subtends a central angle of 360 degrees

so

using proportion

Find out the arc length by a central angle of 168 degrees

[tex]\frac{25.2\pi}{360}=\frac{x}{168}\\\\x=25.2\pi*168/360\\\\x=(25.2*3.14)*168/360\\\\x=36.93\ ft[/tex]

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