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!

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.
RELATED QUESTIONS
In a triangle ABC the lengths of all three sides are positive integers. The point M lies... (answered by greenestamps)

two sides of a triangle have lengths 12 and 15. What are the possible lengths of the... (answered by JBarnum)

Two sides of a triangle have lengths 8 and 11. What are the possible lengths of the third (answered by stanbon)

We are learning about The Triangle Inequality and I am stuck on a question: If the sides (answered by jim_thompson5910)

if the lengths of the sides of a triangle ABC is 3,x+3, and 9 what are all possible... (answered by Edwin McCravy,checkley79)

Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third... (answered by jim_thompson5910)

two sides of a triangle have lengths 6 and 8. what lengths are possible for the third... (answered by rfer,richard1234)

Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third... (answered by Edwin McCravy)

what are all the possible lengths 'x' of the third side of a triangle if the other two... (answered by checkley77,stanbon)