Finding the radius or ѳ

Steps to find the radius or ѳ Bring 360 up and multiply Bring 360 up and multiply Multiply what you can on the right Multiply what you can on the right Divide left side by right side Divide left side by right side

Examples A circle has a central angle of 86 ⁰ and an arc length of 26. Find the radius. What do you need first? The formula!

Example Continued Now follow the steps 1. Bring 360 up and multiply 2. Multiply what you can on the right 3. Divide left side by right side

Another Example What do we know from the question? Plug it in

Another Example Continued Follow the steps Uh oh, we don’t want to solve for r² so how do we solve for r? r = 5.65

More examples = Π10² ѳ = ѳѲ =

Last Example A circle has an arc length of 45 and a radius of 18, what is the ѳ ? = 2Π18 ѳ = ѳ Ѳ = 143.0

6. The area of sector AOB is 48π and. Find the radius of ○ O. m 360 πr2πr2 Area of a sector = πr2πr2 48π = 3 4 r2r2 48 = r2r2 64 = r = 8

7. The area of sector AOB is and. Find the radius of ○ O. m 360 πr2πr2 Area of a sector = πr2πr2 π = r2r2 = r2r2 = 81 4 r = 9 2

Sections Let’s talk pizza

AREA OF SECTION = AREA OF SECTOR – AREA OF TRIANGLE AREA OF SECTOR – AREA OF TRIANGLE ¼ π r² - ½ bh ¼ π r² - ½ bh

Area of section = area of sector – area of triangle area of sector – area of triangle ¼ π r² - ½ bh ¼ π r² - ½ bh 10 A OF = ½∙10∙10= A OF SECTION = 25π - 50 A of circle = 100π A OF = ¼ 100π = 25π 25π

60˚  4 30  O O O Find the area of the shaded region. Point O marks the center of the circle π units 2 9π - 18 units 2 24π - 36√3 units 2 8π - 8√3 units 2

Some common fractions and measures! Arc or Central Angle Measure Fraction of the Circle Arc or Central Angle Measure Fraction of the Circle 36 o 108 o 1/65/6 120 o 2/3 30 o 11/12 1/85/8 1/10 1/3 1/12 3/10 60 o 45 o 300 o 240 o 225 o 330 o