Question

Check my work? Central Angles

Find the measure of the central angle with a radius of 13 inches and the area of a sector measuring 42.25pi square inches.

Answer 1

\[\frac{ 7605 }{ \frac{ 1 }{ 2 } (13^2)}\]


I got this because I translated 42.25pi to degrees (7605)

Answer 2

From there, it should be 90 degrees for the central angle.

Answer 3

@TheSmartOne If you have time?

Answer 4

\(\sf\Large Sector~Area = \frac{\theta}{2}\cdotr^2\)

Plugging in the info given:

\(\sf\Large 42.25\pi = \frac{\theta}{2}\cdot(13)^2\)

Solve for \(\theta\)

Answer 5

I thought sector area was...

\[A = \frac{ 1 }{ 2 }r^2\theta\]

Answer 6

If I follow your equation, I'm looking at... 1.57

Answer 7

Which doesn't seem right.

Answer 8

\(\sf\Large Sector~Area = \frac{\theta}{2}\cdot r^2\)

Plugging in the info given:

\(\sf\Large 42.25\pi = \frac{\theta}{2}\cdot(13)^2\)

Solve for \(\theta\)

Answer 9

The formula you stated is the same.

Answer 10

theta/2 * r^2 = 1/2 * theta * r^2

same thing :P

Answer 11

\[84.5\pi=\theta*169\]

Answer 12

\[84.5\pi/169 = \theta\]

Answer 13

I'm still getting 1.57

Answer 14

why are you making it a decimal?

Answer 15

84.5/169 = 845/1690 = 1/2

Answer 16

It's what my calculator says.

Answer 17

Alright. But 1/2 isn't in degrees. and 50 degrees isn't one of my choices.

Answer 18

@Astrophysics if you get the chance.

Answer 19

It's 1/2 pi

0.5* pi

Answer 20

and that's in radians ^