Question #133042
B. State the Sine Law and the Cosine Law in 3 to 4 sentences.
1
Expert's answer
2020-09-16T20:06:01-0400

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

asinA=bsinB=csinC\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:

AC2=AB2+BC22ABBCcosBAC^2=AB^2+BC^2-2AB*BC*cos B

or

AB2=AC2+BC22ACBCcosCAB^2=AC^2+BC^2-2AC*BC*cos C

or

BC2=AB2+AC22ABACcosABC^2=AB^2+AC^2-2AB*AC*cos A


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