In this page trigonometry we are going to see the history and the definition of angles and their measures.

This word is derived from two Greek words "Trigon" and "metra".This is providing the relationship between the measurements and sides of the angle in a triangle.

**Definition of angle:**

An angle is formed when two rays originate from a common point.One of the rays is called the initial arm and the other ray the terminal arm of the angle.The common point is called the vertex.The rotation of the ray can be performed either in the anti clockwise direction or in a clockwise direction.

If OA and OB are the initial and terminal sides of an angle,then the angle is denoted by the symbol ∠AOB. Sometimes it is convenient to position angle in a Cartesian coordinate plane by taking the vertex at the origin and the initial arm as the positive x-axis when an angle is positioned in the above way.To measure an angle we use as units called degree.

**Degree measure:**

When a ray makes one complete rotation in the anticlockwise direction,we say that an angle of measure 360° is formed.Measurement of all other angles are based on a 360° angle.An angle whose measure lies between 0 degree and 90° is called acute angle. A 90° is called right angle and a 180° angle is called a straight angle.If the sum of two angles is 90° then the two angles are called complementary.When the sum of the two positive angles is 180° the two angles are said to be supplementary.In this topic we must know about the Pythagorean theorem.

The side AC is called the hypotenuse of the right triangle. The side which is opposite to 90 degree is called the hypotenuse side and it is the longest side and is opposite to the right angle. Greek mathematician Pythagoras has found that the length of the square on the hypotenuse is equal to the sum of the length of the squares on the other two sides.

That is,

AC² = AB² + BC². This is knows as Pythagoras theorem.

**Related Topics**

- Trigonometric Ratios
- Trigonometric formulas
- Trigonometric Identities
- Complementary Angles
- Values Of Certain Angles
- Heights And Distances
- Double Angle Formulas
- Half Angle Formulas
- Compound Angle Formulas
- 3A formulas
- Compound angles sum and differences
- Sum to product forms
- Trigonometry-Problems Using Identities
- Trigonometry Practical Problems

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