In trigonometry , how do you find the angles of a right angle triangle?

In order to do that, and this only works for right angled triangles, is using the sine, cosine, and tangent rules. An easy way to remember this is by using the acronym SOH, CAH, TOA that my teacher taught us in school. This equates to Sin x= Opposite/ Hypotenuse (where the opposite is the length of the side of the triangle opposite to the angle which you are trying to find, and the Hypotenuse is the longest side of the right angle triangle, opposite the right angle). By working that out Opposite/ Hypotenuse, using your calculator you would do inverse Sine(O/H) to find the missing angle x. This method can also be used to find the length of one of the sides through manipulating the formula when you are given an angle and one side of the right angle triangle. In which case you can choose which out of the 3 formulas is appropriate. For example, if you are trying to find the adjacent side of the triangle and have been given an angle, you could use the CAH formula, where Cos(90)= x(adjacent)/ hypotenuse. By cross multiplying both sides by the length of the hypotenuse, you would find x which is the length of the adjacent. Therefore, if you have 2 sides of a triangle, you are able to find a missing angle and if you have an angle and 1 side, you are able to find a missing side. This is to not be mistaken for Pythagoras's theorem which can also be used on a right angled triangle, where if you have been given the length of 2 sides, you could use the equation a^2+b^2=c^2 where c is the length of the hypotenuse. It is important to be able to identify what you have been given in a question in order to make a distinction on which method you are able to use to solve it, and also to become familiar with identifying the adjacent, opposite, and hypotenuse sides to use in the given formulas.