Law of Sines or Cosine?

Law of Sines or Cosines?

By KYLA NAULT

Law of Sines or Cosines?

Well, which one is it?

I am not sure if you recall this flow chart that I introduced when I you solve right triangles. The point of the flow chart is to help in deciphering what trigonometric property to use to solve a triangle

Law of Sines

Law of Sines can only be used If and only if there is an opposite pair of angle and side known and then one more piece of information. Take for instance the following slides where you would you Law of Sines

You can see that side u and angle U are both known, perfect Law of Sines set up

​​Perfect Pair

​You will see the only side you know does not initially have an opposite angle, however the angle can be EASILY calculated

A Pair?

Another scenario where that is not initially a side and opposite angle pairing, but one that can be easily found.

A pair?

Can you see how angle W and side w are both known? That's an easy Law of Sines set up!

​​Perfect Match

Law of Cosines

Now to use Law of Cosines, there are two potential scenarios
1. You know all 3 sides
2. You have a "side-angle-side" sandwich

Law of Cosines

Take for instance this triangle, side VU is 19 units long, side TU is 8 units long, and we can see that the angle between them, angle U, is 35 degrees. This creates that "side-angle-side" scenario I mentioned previously. The next slide will have some more examples when you can use Law of Cosines

This scenario, you would want to use Law of Cosines to solve since it is a "side-angle-side" case

Side-Angle-Side

​No if, and, or buts for this problem, We are given all three sides so to solve for WHATEVER angle, you HAVE to use Law of Cosines

All three sides

​This is another side-angle-side case, but I high lighted the known information to see if that helps see the formation of the side-angle-side

Side-Angle-Side

All well and good but now what?

Practice

The goal today is to practice only seeing if you can identify if a problem would be Law of Sines to solve or Law of Cosines to solve! I will be adding in answer explanations so be sure to read those if you are struggling!

Multiple Choice

If I wanted to solve for angle E, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for side u, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for side g, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for angle F, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for side v, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for side v, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for angle X, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines

Multiple Choice

If I wanted to solve for side t, would I need to use Law of Sines or Law of Cosines?

• Law of Sines

• Law of Cosines