MHB Degree Measure of Central Angle

[mathdad]

In a circle of radius 3 meters, the area of a certain sector is 20 m^2. Find the degree measure of the central angle. Round the answer to two decimal places.

Must I use A = (1/2)(r^2)(theta)?

 

[HOI]

You don't have to but you certainly can!

You are told that A= 20 and r= 3. So what is [math]\theta[/math] in radians (the formula you give requires that [math]\theta[/math] be in radians)? And then what is [math]\theta[/math] in degrees?

 

[mathdad]

Theta = 40/9

Theta in degree measure is 254.6°.

Theta in radian measure is 4.444 radians.

 

[HOI]

Yes, that is correct.

 

[mathdad]

Very good.