Answer to Question #133042 in Trigonometry for joseph se

Question

B. State the Sine Law and the Cosine Law in 3 to 4 sentences.

Answer 1

The Sine Law:

Figure 1

When you know 1 side of triangle and its 2 angles and you must find another side, you can use this law. It also works, when you know 2 sides and 1 angle and you need to define another angle.

From triangle ABC (Figure 1) we can write that

$\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}$ .

The Cosine Law:

When you know 2 sides of triangle ABC and one of its angles, you can find the third side using the next formula:

$AC^2=AB^2+BC^2-2AB*BC*cos B$

or

$AB^2=AC^2+BC^2-2AC*BC*cos C$

or

$BC^2=AB^2+AC^2-2AB*AC*cos A$