Question

Find the arc length of a central angle of 36 degrees in a circle whose radius radius in 2 inches.
A.18 in.
B. 2 π/5in
C.72in.
D. π/10in

Answer 1

please, first you have to express your angle in radians, namely
36 degrees hwo radians are?

Answer 2

oops ...how many radians are?

Answer 3

for example 90 degrees are pi/2 radians

Answer 4

1?

Answer 5

no, please if you want to find radians starting from degrees, you have to solve this proportion:
\[180:36= \pi :x\]
please solve for x

Answer 6

do you know how to solve that proportion?

Answer 7

no

Answer 8

please you have to apply the fundamental property of proportions, namely:
product of the means equals the product of the extremes, so:
36* pi= 180*x

Answer 9

\[36* \pi= 180* x\]

Answer 10

now, please divide both sides of that equation by 180

Answer 11

namely:
\[\frac{ 36* \pi }{ 180 }=\frac{ 180 * x }{ 180 }\]
plese simplify that expression

Answer 12

oops ...please simplify ...

Answer 13

36π/180= x?

Answer 14

ok! now what is
\[\frac{ 180 }{ 36 }=...\]

Answer 15

5

Answer 16

perfect so your angle is:
\[x=\frac{ \pi }{ 5 }\]

Answer 17

now by definition of measure of an arc, in order to find the length of your arc, please you have to apply this formula:
\[arc-length=x * radius\]
where x is your angle in radians, so?

Answer 18

what is your arc-length, please?

Answer 19

\[x* radius= \frac{ \pi }{ 5 }*2=...\]

Answer 20

B?

Answer 21

that's right!

Answer 22

Thank you!

Answer 23

Thank you!

Answer 24

use the ratio: angle/360 = length/2*pi*r