I how do I find the angles, if I only know the lengths of the 3 sides?

Thank you for posting your question to the Ask Me Help Desk.

If you are given the lengths of 3 sides of a right triangle...

SinΘ = opp/hyp

This means that if you divide the two lengths that correspond to the side opposite the angle you are looking for and the hypotenuse the answer will be sinΘ. You can then take the inverse sin to solve for Θ.

You can also use

cosΘ = adj/hyp which is the adjacent side to the angle you are looking for and the hypotenuse

tanΘ = opp/adj which is the opposite divided by the adjacent side

Don't forget to take the inverse function to solve for theta.

As rudi_in said, the info he gave is for a right triangle, i.e. one with one angle = 90degrees.
If the triangle is not a right triangle things get much more complex. The info at http://en.wikipedia.org/wiki/Triangle is enough to figure it out. If you need someone to give assistance let us know.

I just found an example of how to find the angles of a triangle given the three side lengths:
http://www.teacherschoice.com.au/Mat...e_trig_SSS.htm

Apply the law of cosines first (to find one of the angles), then apply the law of sines to find the other 2.

Use the Law of Cosines

In any triangle ABC, with sides a, b, and c,
a^2=b^2+c^2-2bc cos A
b^2=a^2+c^2-2ac cos B
c^2=a^2+b^2-2ab cos C

According to the Law of Cosines

In any triangle ABC, with sides a, b, and c,
a^2=b^2+c^2-2bc cos A
b^2=a^2+c^2-2ac cos B
c^2=a^2+b^2-2ab cos C

So if you want find angle A:

From above:

2bc cos A = b^2 + c^2 - a^2

From this equation you can find A

Quote:

---

Originally Posted by DwhiteMann

I how do I find the angles, if I only know the lengths of the 3 sides?

---

If you know the lengths of the sides and want to find the angle measures of a given triangle, use the law cosines.

Here is link:

The law of cosines. Topics in trigonometry

I hope this helps.