I worked out this problem, but I keep getting an odd answer...?

Question

I have a triangle with sides a=10, b=4, and c=6. I've used the law of cosines to find the sides, but every time I try to find one of the angles, it comes out as 180 degrees. Am I doing something wrong, or is it a trick? It says it's an oblique triangle, gives those three sides, and says use the law of cosines. Thanks for any help!

To the first answerer, thanks. I didn't notice, but she never does that, so I'm wondering if it wasn't just a mistake on her part.

To flori, I just plugged in "b" first and tried to find the angle, which came out to a straight line. I plugged in 4^2=10^2+6^2-2(10)(6)(cosB) and it came out to 180 degrees, but I thought I just messed up so I tried for A and it came out the same, so I figured it was just one less problem I have to work out...but what got me was that the instructions says it's oblique. I think she must have just meant to put in different values.

Answer 1

Your "triangle" is a line (i.e., it's what is called a "degenerate case" of a triangle). Think about it, the combined length of sides b and c are equal to the length of side a. That means the angle between sides a-b and the angle between sides a-c must be zero, and the angle between sides b-c must be 180 degrees.

Answer 2

The sum of the lengths of any two sides should always be greater than the length of the third one, so that it would be a triangle, but in your question, 4 +6 = 10, which doesn't fit that rule, so your question either has wrong values, or it has wrong values.

Answer 3

This is a mean problem :) The angles are A = 0, B = 180 and C = 180.

Try to draw this triangle.... It is perfectly flat! You can see that right away by noticing that

a = b + c

Answer 4

6+4=10
when 2 sides add up to the value of the third side, it's a not a triangle... it's a straight line.

Answer 5

can you show how you worked out cosine law for this question ,then i can find where is fault. though with sides 10,4,6 it can't be oblique triangle.