contestada

If the radius of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

a.3 7 ? inches

b.7 2 ? inches

c.7 3 ? inches

d.7 6 ? inches

Respuesta :

Banabanana
[tex]L = \cfrac{ \pi rn}{180} \ \ \ \ \ \ \ [\text{L=arc length, r=radius, n=central angle,} \ \pi \approx3.14 ] \\ \\ \\ L = \cfrac{ 3.14*6*70}{180} \approx7.33 \ in[/tex]
calculista

Answer:

Option C. [tex]\frac{7}{3}\pi \ in[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

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

In this problem we have

[tex]r=6\ in[/tex]

substitute

[tex]C=2\pi (6)=12\pi\ in[/tex]

Remember that

[tex]360\°[/tex] subtends the complete arc of length [tex]12\pi\ in[/tex]

so

by proportion

Find the arc length by an angle measuring [tex]70\°[/tex]

[tex]\frac{360}{12\pi }=\frac{70}{x}\\ \\x=12\pi *70/360\\ \\x=\frac{840}{360}\pi \\ \\x=\frac{7}{3}\pi \ in[/tex]