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A central angle of a circle with radius 150 cm cuts off an arc of 200 cm. Find each measure in Exercises 4 and 5.
4. the radian measure of the angle
5. the area of a sector with that central angle

Respuesta :

Answer:

Part 1) The exact value of the arc length is

Part 2) The approximate value of the arc length is

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5[/tex] [tex]in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi[/tex] [tex]in[/tex]

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

[tex]\frac{10\pi }{360}=\frac{x}{150}[/tex]

[tex]x=10\pi *150/360[/tex]

[tex]x=\frac{25}{6} \pi[/tex] [tex]in[/tex]

step 3

Find the approximate value of the arc length

To find the approximate value, assume

[tex]\pi =3.14[/tex]

substitute

[tex]\frac{25}{6}(3.14)=13.1[/tex] [tex]in[/tex]

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