PreCalcCast Law of Sines

Demo of the ambiguous case for the Law of Sines

Category:

Education

Tags:

• precalculus
• lawofsines

[Eunhyex3]

Hi I have a question about this problem... In the beginning, you said that c is the opposite side (i get this one) and b is the adjacent side... How do you know that b is the adjacent side when you also have side a?

[elmacdork]

If you have all 3 sides (a, b, and c), then you would have to use the Law of Cosines. If it's just one side (b) it really doesn't matter which side you label. For angle C with side c opposite, then the other two sides are adjacent. It won't matter which side we use as b, angle B will be directly opposite.

[sdfjkgrace]

thanks, i really appreciate this step-by-step example.

just wondering, though, how do you know that the ambiguous case applies? what if there's no solution -- how would you know?

[elmacdork]

A "No Solution" would have an "error" when we went to the calculator to inverse the ratio. As far as the ambiguous case, there are several ways to check, but in general: if the opposite side is smaller than the adjacent side, there are usually 2 solutions.

[sdfjkgrace]

well because in your video it says it can be either 0 or 2, so how can you tell which it is?

[elmacdork]

Since the opposite side is smaller than the adjacent, there are either 0 or 2 solutions. When we set up the law of sines and do the inverse to find the angle, we get a solution. Therefore there must be another one.

If we set up the law of sines and do the inverse to find the angle and we get an error (domain) then there is no solution.

[jacksong00]

Thank Man, but instead of writing 57, you wrote 75. Just want to show you your little typo.

[happylarosa]

my teacher has been trying to explain this for a few days and it only just makes sense thanks so much!

[sdfjkgrace]

ohhh, okay. :) thank you so much!

[theyova88]

You should be careful with your significant figures...you cant get more accurate than what you are given...