# How to find the angle, if we know the side of a right triangle

Triangle, one corner of which is straight (equal to 90 °), referred to as rectangular. Its longest side is always opposite the right angle is called the hypotenuse, and the other two sides are called legs. If the lengths of the three sides are known, then find the value of all the angles of a triangle is not difficult, because in fact need to calculate only one of the corners. You can do this in several ways.

## Instruction how to find the angle, if we know the side of a right triangle

Step 1:

Is used to calculate values of angles (α. β. γ) Definition of trigonometric functions using right-angled triangle. Such a definition, for example, an acute angle sine formulated as a ratio of the length of the opposite leg to the length of the hypotenuse. So, if we know the length of the legs (A and B) and the hypotenuse (C), then find, for example, the sine of the angle αLying in front of leg A, separate the length of side A on the length of the side C (the hypotenuse): sin (α) = A / C. Learning the value of the sine of the angle you can find its value in degrees, using the inverse sine function - arc sine. I.e α= Arcsin (sin (α)) = Arcsin (A / C). In the same way it is possible to find the size and other sharp angle in the triangle, but this is not necessary. Since the sum of the angles of a triangle is always 180 °, and in a right triangle is equal to one of the angles 90 °, then the value of the third angle can be calculated as the difference between 90 ° and the angle magnitude found: β= 180 ° -90 ° -α= 90 ° -α.

Step 2:

Instead of defining the sine can use the definition of cosine acute angle, which is formulated as a ratio of the length of the adjacent leg to the desired angle to the length of the hypotenuse: cos (α) = B / C. Here engage inverse trigonometric functions (inverse cosine) to find the angle in degrees: α= Arccos (cos (α)) = Arccos (B / C). After that, as in the previous step will be to find the value of the missing angle: β= 90 ° -α.

Step 3:

You can use the same definition of tan - it is expressed by the length of the opposite corner of the desired leg to the length of the adjacent leg: tg (α) = A / B. The angle in degrees is again determined by inverse trigonometric functions - the arc tangent: α= Arctg (tg (α)) = Arctg (A / B). The formula of the value of the missing angle remains unchanged: β= 90 ° -α.