# The largest angle in a triangle:

• joelio36
In summary, the largest angle in a given triangle is always opposite the longest side. This can be found using the law of sines for acute triangles or the cosine rule for obtuse triangles. The largest angle will always be the angle opposite the largest side, regardless of the size of the triangle.
joelio36
I have a triangle, with sides 8.5, 6.8, and 9.4, what is the largest angle?

I think that it will always be the angle opposite the longest side, and used the cosine rule from there, along with trig identies to find the largest possible angle (<180).

Is this a correct method?

Just use the http://en.wikipedia.org/wiki/Law_of_cosines" to find each angle. Then you will be able to say which one is the biggest.

Last edited by a moderator:
You' re absolutely wrong! You can have a big side with a small angle as its opposite.
I think you'll have to calculate, no general way to do it. :)

Stick by the cosine rules and you'll be fine.

joelio36 said:
I have a triangle, with sides 8.5, 6.8, and 9.4, what is the largest angle?

I think that it will always be the angle opposite the longest side, and used the cosine rule from there, along with trig identies to find the largest possible angle (<180).

Is this a correct method?
Yes, in a given triangle the longest side is always opposite the largest angle. Just use the cosine rule for that side.

stingray78 said:
You' re absolutely wrong! You can have a big side with a small angle as its opposite.
I think you'll have to calculate, no general way to do it. :)
Sorry, but you are the one who is "absolutely wrong". You might be thinking that if the triangle is very large then a side opposite a small angle can be "big"- but in that case the other sides will be even larger.

stingray78 said:
You' re absolutely wrong! You can have a big side with a small angle as its opposite.
I think you'll have to calculate, no general way to do it. :)

The largest side is always opposite the largest angle. consider a triangle with angles
A,B and C and the side a opposite to the angle A etc.

For acute triangles you can get this from the law of sines: $$\frac{a}{sinA} = \frac{b}{sinB}$$, so if a>b then a/b>1 and so $$\frac{sinA}{sinB} > 1$$ therefore sin(A) > sin(B). since sin is increasing from 0 to 90 degrees this implies A>B

For obtuse triangles there can be only one obtuse angle, which must be the largest. call this A. cos(A) < 0 sothe cosine rule tells us that a^2 > b^2 + c^2 and therefore a>b and a>c so the largest angle is also to the opposite of the largest side.

P.S. Is there a way to get tex fractions lined up with the line of text they are in?

Hehehe sorry, you're right. Didn't give it enough thinking. I was the one absolutely wrong. Sorry!

## 1. What is the largest angle in a triangle?

The largest angle in a triangle is always opposite the longest side, also known as the hypotenuse.

## 2. How do you find the largest angle in a triangle?

To find the largest angle in a triangle, you can use the Law of Cosines or the Law of Sines, depending on the information given.

## 3. Can the largest angle in a triangle be greater than 90 degrees?

No, the largest angle in a triangle cannot be greater than 90 degrees. In fact, the sum of all angles in a triangle must equal 180 degrees.

## 4. Is the largest angle in a triangle always the same?

No, the largest angle in a triangle can vary depending on the lengths of the sides. A triangle can have three different largest angles depending on the ratio of the side lengths.

## 5. Why is the largest angle in a triangle important?

The largest angle in a triangle is important because it helps determine the shape and properties of a triangle. It is also necessary for solving many mathematical and geometric problems involving triangles.

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