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# Math

## Trigonometric Ratios and Pythagorean Theorem

##### 1) Sine of an angle: In a right triangle, the sine or sin of an angle is the ratio of the side opposite to the angle to the hypotenuse: ##### 2) The Cosine of an angle: In a right triangle, the cosine or cos of an angle is defined as the ratio of the side adjacent to an acute angle to the hypotenuse. ##### 3) Tangent of an angle: Tangent or Tan of an angle is defined as the ratio of the side opposite to an angle to the side adjacent to the angle. ##### 4) Cotangent of an angle: Cotangent or Cot of an angle is defined as the ratio of the side adjacent to an angle to the side opposite to the angle. ##### 5) Cosecant of an angle: Cosecant or Csc of an angle is defined as the ratio of the hypotenuse to the side opposite to the angle. ##### ##### Example: Find the trig ratios of the given angle.   ##### Example: In the triangle shown below, find the value of x.  ## Pythagorean Theorem

##### The Pythagorean theorem states a fundamental relationship between three sides of a right triangle. According to this theorem, the area of a square whose side is the hypotenuse  is equal to the sum of the areas of the squares whose sides are the other two sides of a right triangle. ##### Example: Find the unknown side of the triangle below. ##### We use the Pythagorean theorem to find c: 