How to find 3 triangle angles with 3 sides given

[Dan Ebberts]

Like this, I think:

a =16;
b = 20;
c = 18;
A = radiansToDegrees(Math.acos((b*b + c*c - a*a)/(2*b*c)));
B = radiansToDegrees(Math.acos((a*a + c*c - b*b)/(2*a*c)));
C = radiansToDegrees(Math.acos((a*a + b*b - c*c)/(2*a*b)));

[Mikael Holmström]

Lovely, thank you very much!

Mikael

[mike kleni]

Starting with your last question: Note that “height” (or altitude) will be relative to a specific side of your triangle. If you don’t specify which of the three sides you’ve chosen, then we can’t know whether your height is correct relative to that side.

For your other questions: I’d recommend using the Law of Cosines to compute the measures of the respective angles. I’m getting different answers from yours. This make sense intuitive sense: angle A is opposite the shortest side, so it should be the smallest of the three angles. That wasn’t what you found, though. Important note: When computing the relevant inverse cosines, make sure your output is in degrees or radians, depending on what the exercise specifies.

For the area of the triangle, you have a few options. One is to compute one of the angles, then use that to compute the triangle’s area, given that you know the measure of an angle and the lengths of the two adjacent sides. Alternatively, you can use Heron’s Formula, which requires only the lengths of the three sides (though it can be a more obscure formula, depending on your background). Hope this helps. Good luck!