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SS2 Mathematics Third Term: Trigonometry: Derivation of Sine Rule and Application; Derivation of Cosines Rule and Application

Introduction

The sine rule formula states that the ratio of a side to the sine function applied to the corresponding angle is same for all sides of the triangle. For a triangle ABC, sine rule can be stated as given below:

tttt1

The sine rule formula can be used to find the measure of unknown angle or side of a triangle. It can be used to predict unknown values for two congruent triangles.

If for a given triangle, a, b, and c are the lengths of sides , and A, B, and C are the opposite angles then the sine rule formula is also stated as the reciprocal of this equation:

tttt2

triangle

 

Derivation of Sine Rule

To derive the formula, erect an altitude through B and label it hB as shown below. Expressing hB in terms of the side and the sine of the angle will lead to the formula of the sine law.

First figure for the derivation of sine law

 

L

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SS2 Mathematics Third Term: Trigonometry: Derivation of Sine Rule and Application; Derivation of Cosins Rule and Application

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