# Thread: Determine Angle Type Given Side Lengths

1. ## Determine Triangle Type Given Side Lengths

How can you determine if a triangle is obtuse or acute given the three side lengths?

For example, given side lengths of "14, 21, and 25", how can you determine the type of triangle?

Thanks!

2. Hi math20,
Use the law of cosines. This is trig.Look up the formula which varies for each angle.After calculating one angle the sine law can be used for the other angles

bjh

3. Originally Posted by mathguy20
How can you determine if a triangle is obtuse or acute given the three side lengths?
For example, given side lengths of "14, 21, and 25", how can you determine the type of triangle?
Hope you know the law of cosines: $\displaystyle c^2=a^2+b^2-2ab\cos(\theta)$.
You know that the longest side is opposite the largest angle.
So suppose that $\displaystyle c\ge b\ge a$.
If $\displaystyle \cos(\theta)<0$ then $\displaystyle \theta$ is obtuse.

4. bjhopper and Plato, thanks for the quick responses!

So per my example, using the law of cosines, the angle would be approximately 88.8° (and thus the triangle = acute)?

5. Originally Posted by mathguy20
bjhopper and Plato, thanks for the quick responses! So per my example, using the law of cosines, the angle would be approximately 88.8° (and thus the triangle = acute)?
I am not at all sure what that means.
If $\displaystyle a^2+b^2-c^2<0$ then the triangle is obtuse.

6. Originally Posted by Plato
I am not at all sure what that means.
If $\displaystyle a^2+b^2-c^2<0$ then the triangle is obtuse.
Got it -- In my original problem, you'd get $\displaystyle 14^2+21^2-25^2=12$, which is greater than 0 and therefore acute.

In my last post, I meant that if we look back at my original example, we can solve angle C to be approximately 88.8 degrees, and therefore the triangle would be acute? Is that another method to solve the problem?

7. Hi mathguy20 and Plato too,

Sides of triangle are a= 14 b= 21 c= 25 Angle A is opposite c
I calculate angle A is 88.8 degrees so the triangle is acute

another method
drop an altitude to a side Using Pytag write two equations in x for the alt segments and alt h. Solve for x and the other segment. Calculate angles using trig functions

bjh

8. Hello, mathguy20!

How can you determine if a triangle
is obtuse or acute given the three side lengths?

For example: given side lengths of 14, 21, and 25,
how can you determine the type of triangle?

Square the longest side; call this $\displaystyle \,x.$

Find the sum of the squares of the other two sides; call this $\displaystyle \,y.$

. . If $\displaystyle x > y$, obtuse triangle.
. . If $\displaystyle x < y$, acute triangle.
. . If $\displaystyle x = y$, right triangle.

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# how to tell what type of triangle it is just from side lengths

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