How to find the angle of a triangle
In geometry problems for different classes, the goal or intermediate action is to find the angle of the triangle. Let's see how this is done in different types of triangles.
Universal formulas to find out the angle of a triangle
The formulas below will work for any type of triangle.
- ∠A = 180°-(∠B+∠C) (since the sum of all angles of a triangle is 180°).
- ∠A = 180°-∠OAB (because ∠OAB is external).
Find out the angle in an isosceles triangle
An isosceles triangle can be identified by two equal sides or two equal angles.
- ∠B = 180°-2 ∠A.
- ∠A = ∠C (because the angles at the base of an isosceles triangle are equal).
- If ∠A=60°, then all angles are 60° and triangle ABC is equilateral.
Find an angle in a right triangle
The angles in a right triangle can be found either by one of the methods presented in paragraph 1, or using trigonometric functions - sine, cosine, tangent and cotangent.
Trigonometric functions
If you are given two sides, you can find the angle using the following algorithm:
- We look at what these sides are in relation to the right angle (leg, hypotenuse) and the angle to be found (adjacent/opposite leg).
- We find a trigonometric function that suits us.
- We find what it is equal to by substituting the values of these sides.
- We calculate the angle using the inverse function (arcsine, arccosine, etc.).
Sine and cosine theorems
You can see the theorems in the picture below. With the help of them, you can find out the cosine or sine of the angle you are interested in, and calculate the value through it.
