How to Solve a Triangle Knowing Three sides. Check out this triangle solver

A triangle calculator will help you find all the parameters of a triangle, knowing only some initial information about the triangle

Indeed, a triangle has 3 angles and 3 sides when it is completely determined, and using different trigonometric and geometric properties, it is enough to know three of those parameters in order to determine the other three.

But it is not just any three pieces of information. You have to have either: two sides and an angle, or two angles and a side or you need to have three sides. This calculator shows how to work out the case when know you the three sides.

Are three pieces of information always sufficient?

No. For example, having the three angles of a triangle is not enough to determine the sides. Why, would you ask? If having three angles means that I have three pieces of information?

What happens is that we know that the sum of the three angles will be 180^o degrees (or \(2\pi\) radians), so then we only have two pieces of information really, because the third angle we directly derive from the other two.

Finding missing sides and angles

So, what do you do when you have partial information about a triangle? The answer is: it depends on the situation. Depending on whether you have the SAS, SSA, SAA or the SSS cases, you will use different tools.

So indeed, depending on the case, you will apply a combination of the law of sines and law of cosines, in order to find the missing triangle information.

Once you have found the missing parts (sides and/or angles) you can compute both the perimeter and area of the triangle.