Al-Huda Science Academy has created Math Class 11 Chapter 12 Formulas for better trigonometric ratios understanding.

## Math Class 11 Chapter 12 Formulas

### THE DISTANCE FORMULA

*Let A(*x_{1}, y_{1}*) and B(*x_{2}, y_{2}*) be any two points on the plane, then*

|**AB**| = √(x_{2}− x_{1})^{2}+ (y_{2}− y_{1})^{2} *is called as the distance formula. Where |*AB| *indicates the distance between A and B.*

### THE LAW OF SINES

*The measures of sides are proportional to the sines of the measures of opposite angles.*

*Note:** Suppose that according to the above figure if* a/sinα = 10, then b/sinβ and c/sinγ are also equal to 10.

### THE LAWS OF COSINES

a^{2} = b^{2} + c^{2} – 2bcCosα

b^{2} = c^{2} + a^{2} – 2caCosβ

c^{2} = a^{2} + b^{2} – 2abCosγ

*The laws of cosines can also be written as follows in order to measure the angles*

### THE LAWS OF TANGENTS

**NOTE: – ***The law of Sines and the Laws of Cosines and Tangents are used to find the remaining elements of a triangle.*

### Pythagoras Theorem

### Half Angle Formulae In Terms Of The Lengths Of The Sides Of A Triangle

*Tangent formulas can also be written as*

**Note: **These formulas are used to find the angles when three sides of triangle are given.

### Area Of A Triangle And Its Formulas In Various Cases

__Area of a triangle__: – *The area of a triangle is the number of square units insidethat triangle. It is denoted by filled triangle i.e., “∆”. *

*The general formula for measuring it is*:

* ***Area =**** *** Where, “ b” is the base and “a” is the corresponding altitude of the triangle.*

*In trigonometry area of triangle is being measured by various ways and formulas depending upon the given conditions. At this stage there are three main cases based on given data.*

**CASE I: –**

*When the measures of two sides and the measure of the included angle are known.*

**CASE II: –**

*When the measures of two angles and the measure of one side are given.*

**CASE III: – **

*When the measures of all three sides are known.*

*where “s” semi-perimeter*

**Note**: *This is also known as Heron’s Formula*