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How to find the angle in a right triangle

How to find the angle in a right triangle

Already from the name "square" of the triangle becomes clear that one corner it was 90 degrees.

The rest of the corners can be found by remembering some simple theorems and properties of triangles.

You will need

  • Table of sines and cosines, Table Bradis



Denote the angles of the letters A, B and C, bothIt is shown. Angle BAC is 90º-, two other angle denoted α- letters and β-. Catete triangle denote the letters a and b, and hypotenuse of the letter c.

In this figure, all the symbols that will be used in the article


Then sinα- = b / c, and cosα- = a / c.

Similarly, for the second acute angle of the triangle: sinβ- = a / c, and cosβ- = b / c.

Depending on what side we know, we calculate sines and cosines of the angles and look at the table Bradis value α- and β-.


Finding one of the corners, you can remember that the sum of the triangle interior angles is 180º-. Hence, the sum of α- and β- equal 180º- - 90º- = 90º-.

Then, by calculating a value for the .alpha.-tables, we can to find the .beta.-use the following formula: β- = 90º- - α-


If you are not one of the sides of a triangle, thenWe use the Pythagorean theorem: a²- + b²- = c²-. Derive from it the expression for the unknown side over the other two and substitute into the formula for finding the sine or cosine of one of the corners.

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