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# How to find the angles of a triangle on the sides

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A triangle is the simplest polygon bounded on a plane by three points and three segments pairwise connecting these points.

Angles in the triangle are sharp, blunt and straight.

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

You will need

• Basic knowledge in geometry and trigonometry.

Instructions

1

Denote the lengths of the sides of the triangle a = 2, b = 3,C = 4, and its angles are u, v, w, each of which lies opposite to one side. By the cosine theorem, the square of the length of the side of the triangle is equal to the sum of the squares of the lengths of the other two sides minus the doubled product of these sides by the cosine of the angle between them. That is, a ^ 2 = b ^ 2 + c ^ 2 - 2bc * cos (u). We substitute the lengths of the sides into this expression and get: 4 = 9 + 16 - 24cos (u).

2

We express cos (u) from the resulting equality. We obtain the following: cos (u) = 7/8. Next, we find the angle u itself. For this, we calculate arccos (7/8). That is, the angle u = arccos (7/8).

3

Similarly, by expressing the other sides through the rest, we find the remaining corners.

How to find the angles of a triangle on the sides Was last modified: June 21st, 2017 By
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