How to determine angles in a right triangle

The rectangular triangle is characterized by certain relationships between the angles and sides. Knowing the meaning of some of them, you can calculate the other. For this purpose, formula, based, in turn on the axioms and theorems of geometry.

Instruction

1. From the name of a right triangle it is clear that one of its angles is a direct. Regardless of whether it is an isosceles right triangle or not, it always has one angle equal to 90 degrees. If given a right triangle that is both isosceles and then, based on the fact that the figure is a straight angle, find two angles at its base. These angles are equal, so each of them has a value equal to:
   
   α=180°- 90°/2=45°
2. In addition to the above, it is also possible the other case, when the triangle is rectangular, but is not isosceles. In many problems the angle of the triangle is 30° and the other 60°, because the sum of all angles in a triangle must equal 180°. If given the hypotenuse of a right triangle and side angle can be found from matching the two sides:
   
   sin α=a/c where a is the side opposite to the hypotenuse of a triangle, with the hypotenuse of the triangle
   
   Accordingly, α=arcsin(a/c)
   
   Also the angle you can find the formula for cosine:
   
   cos α=b/c where b is the adjacent side to the hypotenuse of the triangle
3. If you know only two sides, the angle α can be found according to the formula of the tangent. The tangent of this angle is equal to the ratio of opposite over adjacent:
   
   tg α=a/b
   
   From this it follows that α=arctg(a/b)
   
   When the straight angle and one of the corners found by the above method, the second is as follows:
   
   ß=180°-(90°+α)