How Do You Calculate the Angle and Area in Trigonometry Problems?

[rocomath]

Homework Statement

32. Three gears are arranged as shown in the figure below. Find the angle $$\phi$$

46. Prove that the area of a parallelogram is the product of two adjacent sides and the sine of the included angle.

Homework Equations

The Attempt at a Solution

32. I assumed that since the gears touch that I could add their radius. Would that be incorrect? I was thinking I had to use the linear and angular speed formulas, but I wasn't sure. I know that their linear speed is equal, but I don't think I need to do all that.

46. I followed the steps in which they obtained the Area of a triangle.

 

[Gib Z]

Both workings seem find to me.