For which measures of the sides of triangle ABC is angle B the largest angle of the triangle?
1. AB=2, BC=6, AC=7
2. AB=6, BC=12, AC=8
3. AB=16, BC=9, AC=10
4. AB=18, BC=14, AC=5
i dont know how to do this it doesnt evne give me any numbersss
Well, you could use the law of cosines to figure it out. Or, what your instructor is probably looking for you do use is one of the theorems/postulates. I know what that theorem says, but I unfortunately can't remember the same of it. The theorem says that "the largest angle will always occur opposite the largest side".
Thus, you have to consider, for angle B, which triangle has side AC as the largest side. That would only be triangle #1, tied with angle A, which is opposite side BC.
You may consider the triangle I have labelled on the attachment. Normally, they aren't labelled like this. Normally, they would have "side A" opposite "angle a" But, you have the sides labelled with 2 letters here. So, I am assuming it is a triangle labelled as such.
In a triangle, there always exists this rule:
The side opposite of the angle with the largest value has the largest value.
The inverse of this works, as well.
The angle opposite of the side with the largest value has the largest value.
Let me draw a picture for you.
As you can see from the picture, AC is the largest side.
Now, we have to look at one of the choices that satisfies this statement.
1. Is the only statement that satisfies this, (according to your correction)
Hope I helped!
Thefirst answer is correct. They have given you the length of each side....represented by the two capital letters. For angle B to be the largest angle, the opposite side (represented by AC) would need to be the longest side. In this answer, AB=2, and BC=6. Because AC=7, and this is the longest side, B would be the largest angle.
Using the below link you can easily find the biggest angle.
1. AB=2, BC=7, AC=7 the angle B =`110^o`
2. AB=6, BC=12, AC=8 the angle B= `36^o`
3. AB=16, BC=9, AC=10 the angle B= `35^o`
4. AB=18, BC=14, AC=5 the angle is B= `11^o`
so, we can easily say that option 1 is the correct answer.