7-2

In this section, there are three formulas you can use:

• K = 1/2r^2theta (theta is a circle with a line through it, but I don't know how I could put that on here so...i just wrote it out). K stands for the area of a sector. R stands for the radius and Theta stands for the central angle.
• K = 1/2rs. In this formula, R stands for the radius and S stands for the are length.
• S = rTheta. S is the are length, R is the radius, and Theta is the central angle.

Apparent Size:

• S = rTheta: R is the distance between two objects, Theta is the apparent size, and S is the diameter of the object.

Ex. A sector of a circle has an arc length of 10cm and an area of 55cm^2. Find the radius and the measure of its central angle.

1. First you need to identify the things you already have and what you need.

• S = 10cm
• K = 55cm^2
• R= ?
• Theta = ?

2. Now you need to figure out what formula you can use for this word problem.

• You can use K = 1/2rs.
• You can also use S=rtheta.

3. Now you need to plug in the numbers you have into the first problem.

• Since you are trying to find your Radius, you need to solve for R.
• You will end up with 2k = rs. (you divided by 2 on each side to get that).
• Now you need to get R on the side where the 2k is. You divide each side by S. You end up with R = 2k/s.
• Now you plug in your numbers. R = 2(55)/10.
• Your final answer is R = 11.

4. Now you have to find Theta.

• Use the equation S= rtheta.
• You have to solve for Theta. So your equation will now be: Theta = S/R.
  
• You plug in your Radius and arc length into the problem.
• Theta = 10/11
• Final answer: Theta = 10/11 rads.

-Amber :)