Question

find the length of the arc question 32 pic below @jim_thompson5910

Answer 1

The square marker means we have a 90 degree angle

Answer 2

if there are 360 degrees in a full circle, then what must this remaining angle be?

Answer 3

Wow Im an idiot sometimes it would have to be 270

Answer 4

yes 270 degrees

Answer 5

what is the circumference of the circle if the radius is 18?

Answer 6

the final answer isn't 270 btw, but it helps us get there

Answer 7

aw man I thought it was going to be simple

Answer 8

do you remember the formula for the circumference of the circle?

Answer 9

113.09 for circumference

Answer 10

leave it in terms of pi

Answer 11

C=2pixr

Answer 12

think of pi as a variable

Answer 13

36pi

Answer 14

right?

Answer 15

good

Answer 16

36pi is the exact total distance around the FULL circle

but we just want a piece of the circle. The red piece

so we multiply the circumference by (270/360) which is the same as multiplying by (3/4)

notice how 270/360 reduces to 3/4

so it makes sense that the red piece is 3/4 of the full circle

Answer 17

the arc length formula is...

\[\Large s = \frac{x}{360}*C\]

where

s = arc length
x = central angle
C = circumference of the full circle

Answer 18

ok so s=x/360x36pi what is the cental angle?

Answer 19

in this case, 270 degrees

Answer 20

because 360-90