Easy geometry question?

Question

How do I determine if a triangle is acute when given the three side lengths?

I kind of forgot, thanks!

Haha I knew someone would say less than 90 degrees thinking I meant angles... owell thanks to the 3rd answerer I got it!

Answer 1

First check that the three lengths can actually make a triangle...The two short sides added together have to be longer than the longest side.
Then it's sort of like the Pythagorean theorem... a and b are the two shortest sides and c is the longest side.
If a^2 + b^2 > c^2 then the triangle is acute
If a^2 + b^2 = c^2 then the triangle is right
If a^2 + b^2 > c^2 then the triangle is obtuse

Answer 2

If a triangle is acute, that means the biggest angle is less than 90. That also means the biggest side in the triangle must be opposite an angle less than 90. So by the law of cosines

c^2 = a^2 + b^2 -2abcos(C)

Where c is the length of the biggest side. If you solve that equation for angle C and get a number less than 90 degrees, then the triangle is acute.

Answer 3

Just remember that a right triangle is also an acute triangle because it has 2 acute angles.

Using this info and the fact that a right triangle follows the Pythagoren theorem, see if c^2(the longest side) is less than the sum of the squares of the two other sides, a^2 + b^2.

or c^2 < a^2 + b^2.

For example, c=4.8, a=3 b =4. Note that the longest side is c and that is less than the squares of a and b.

So, if you forget again, just think of Phytagorean Theorem.

Answer 4

If you have a, b, c as the 3 side lengths, without checking to see which one is the largest or smaller, the following formula will work:

(a² + b² - c²) (a² - b² + c²)(- a² + b² + c²) > 0 Acute
(a² + b² - c²) (a² - b² + c²)(- a² + b² + c²) = 0 Right
(a² + b² - c²) (a² - b² + c²)(- a² + b² + c²) < 0 Obtuse

This is a faster way for computer programs to check for type, as the only decision tree involved is whether it's positive, 0, or negative.

Answer 5

If the sum of the squares of the 2 shorter sides is smaller than the square of the longest side, then the triangle is acute.

Answer 6

Intuition tells me that if you add the squares of the shorter sides and divide the sum by the square of the longest side, you'd have this:
>1: obtuse
=1: right
<1: acute.

But my intuition isn't always right, and I've not really checked it out ...

Answer 7

These other guys are dumb. All u have to do is find the tangent of the opposite angle of the smallest side.

Answer 8

IF IT'S LESS THAN 90 DEGRESS HUN.. NO PRB.