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How to find the angles of a triangle on the sides

How to find the angles of a triangle on the sides

Triangle - is the simplest polygon bounded on the plane by three points and three segments mutually connecting these points.

The angles in a triangle are acute, obtuse and straight.

The sum of angles in a triangle is constant and equal to 180 degrees.

You will need

  • Basic knowledge in geometry and trigonometry.

instructions

1

Let the length of the sides of a triangle, a = 2, b = 3,c = 4, and its angle u, v, w, each of which lies opposite the one side. By the theorem of the cosine square of the length of the triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the sides of the cosine of the angle between them. That is, a ^ 2 = b ^ 2 + c ^ 2 - 2bc * cos (u). Substituting in this expression and obtain the lengths of the sides: 4 + 9 = 16 - 24cos (u).

2

We express from the resulting equality cos (u). We get the following: cos (u) = 7/8. Next, we find in fact the angle u. To do this, we calculate the arccos (7/8). That is, the angle u = arccos (7/8).

3

Similarly, expressing the other side through the other, we find the remaining corners.

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