How to find the angles of a triangle on the sides

The triangle is the simplest polygon, bounded on the plane, three points and three segments connecting pairs of these points. The angles in a triangle are acute, obtuse and straight. The sum of the angles in a triangle is constant and equal to 180 degrees.

You will need

• Basic knowledge in geometry and trigonometry.

Instruction

1. Let us denote the lengths of the sides of a triangle a=2, b=3, c=4, and angles u, v, w, each of which lies opposite one of the sides. Cosine theorem the square of the length of the sides of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of these sides into the cosine of the angle between them. That is, a^2 = b^2 + c^2 - 2bc*cos(u). Substitute into this expression the lengths of the sides and get: 4 = 9 + 16 - 24cos(u).
2. Express from the equality cos(u). Will receive the following: cos(u) = 7/8. Then find the actual angle u. To do this, we calculate arccos(7/8). That is, angle u = arccos(7/8).
3. Similarly, expressing the other side through the other, find the remaining angles.