How to find out the triangle angle

In the objectives of geometry for different classes the purpose or intermediate action is to find the corner of the triangle. We will analyze how this is done in different types of triangles.

1

Universal Formulas to find out the triangle angle

The formulas below are suitable for any type of triangles.

• ∠A \u003d 180 ° - (∠В + ∠С) (because the sum of all the corners of the triangle is 180 °).
• ∠A \u003d 180 ° -∠oab (because ∠oab external).

2

Find an angle in an equilibried triangle

An equally chaired triangle can be identified by two equal side sides or two equal corners.

• ∠B \u003d 180 ° -2 • ∠a.
• ∠A \u003d ∠С (because the angles at the base of an inaccessible triangle are equal to).
• If ∠a \u003d 60 °, then all the angles are 60 °, and the ABC triangle is equilateral.

3

Find an angle in a rectangular triangle

Corners in a rectangular triangle can be found either in one of the methods presented in paragraph 1 or using trigonometric functions - sinus, cosine, tangent and catangent.

Trigonometric functions

If you are given two sides, you can find an angle according to the following algorithm:

• We look at what the parties are in relation to the direct corner (catat, hypotenuse) and the corner to find (adjacent / opposite catat).
• We find a trigonometric function that suits us.
• We find what it is equal to, substituting the values \u200b\u200bof the parties.
• Calculate the angle with the help of a feedback (arcsinus, arquosine, etc.).

Sinus and cosine theorems

Theorems themselves you see in the picture below. With the help of them, you can learn cosine or sine angle of interest to you, and to calculate the value.