Question

Could I find the two missing angle measures if I know some of the side lengths of a right triangle?

Answer 1

If you have a right triangle and you know 2 sides (or a side and the hypotenuse) you can find the 3rd using pythagoras.

Now any of your trig functions can be used to find the angles (other than the 90 deg one, which you already know)

Answer 2

Yes. Let's say that you have a triangle ABC where C is the right angle. You want to find angle A, and you know AC = 4 and AB = 5.

Well, if you're standing on angle A, then you know the adjacent side to A (AC) and you know the hypotenuse of the triangle (AB). (Note: You can actually figure out the third side using pyth. theorem, but you don't need to).

Well, we have a trig function involving the adjacent and hypotenuse sides: cosine. We know that the cosine of an angle is equal to the adjacent side divided by the hypotenuse. In short, cos(A) = 4/5.

But how does that help us solve for A? Well, there's a function that does the exact inverse of cosine called inverse cosine, or arccosine. To solve for A, you take the ratio and the angle, you switch them, and you replace the tan function with its inverse.

So cos(A) = 4/5 becomes arccos(4/5) = A. Now it's a matter of putting exactly that into your calculator (which should have a cos^-1 button).