SOLUTION: Hey i have a question! So the sides of an AngleABC lengths are 3,4 and 5. What are the three possible values of the cosine of angle A? I am really stuck!

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Question 600414: Hey i have a question!
So the sides of an AngleABC lengths are 3,4 and 5. What are the three possible values of the cosine of angle A? I am really stuck!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Well assuming you have a right triangle ABC where B is the right angle, you can have two possible triangles:

AB = 3, BC = 4, AC = 5

or

AB = 4, BC = 3, AC = 5

The reason why AC is stuck at 5 is because the hypotenuse is always the longest segment of any right triangle.

So

cos(A) = adjacent/hypotenuse = AB/AC = 3/5

which means cos(A) = 3/5

or

cos(A) = adjacent/hypotenuse = AB/AC = 4/5

which means cos(A) = 4/5

and that's about it.

So either there's a typo and you only need to find two possible values of cos(A) or this triangle isn't a right triangle.

Let's assume that there isn't a typo. This would mean that this isn't a right triangle. But this has to be a right triangle because these three values are a Pythagorean triple (also, ). So that's why I'm convinced that there's a typo.