Calculate the interior angles of a triangle

Even if trigonometric functions and the consideration of a triangle are compulsory in school mathematics heard, it is not that easy to guess how to calculate the interior angles of a triangle can. However, knowing that in a triangle the sum of all angle is always 180 degrees and knows the right formulas, can solve them correctly and then with that calculator can calculate, it is no longer as difficult as initially feared.

What you need to know about triangles

• The sum of all interior angles of a triangle is always 180 degrees.
• Label the points of the triangle A, B, and C counterclockwise.
• Side a faces point A, b faces B, and c faces C.
• The angles at points A, B, and C are called α, β, γ (alpha, beta, gamma).


The law of sines in a non-right-angled triangle - the formula explained using an example

You can also calculate with the trigonometric functions sin and cos in a triangle that is not right-angled: A...

How to calculate the interior angles of a triangle

1. It is best to first calculate the largest angle, which is always opposite the longest side. In this example, this should be side a.
2. Since you initially only know the side lengths of the triangle (which you e.g. can measure with a simple ruler), you need the law of cosines, on one side two Sides and the included angle stand, on the other side the opposite side of the angle, e.g. B. a² = b² + c² - 2bc * cos α.
3. Solve this equation for the angle: cos α = (b² + c² - a²) / 2bc. This results in α = arccos ((b² + c² - a²) / 2bc). If you die Dimensions of a, b and c, you can enter them all into the calculator.
4. You can of course calculate the other angles in the same way. But since you now know an angle, you can use the 2nd Calculate interior angles more easily, namely using the law of sines. This means that the ratio of the length of one side to the sine of the opposite angle is always the same: i.e. a / sin α = b / sin β = c / sin γ.
5. so you can calculate β: a / sin α = b / sin β. This results in sin β = sin α * b / a, i.e. β = arc sin (α * b / a). Enter everything back into the calculator.
6. Now that you know two angles, you can easily calculate the last one knowing that all three angles together must be 180 degrees by dividing the first two angles from 180 degrees pull it off.

It may seem complicated at first, but once you get the hang of it, it's actually quite easy to calculate the interior angles of a triangle.