Unit A: Geometry

Chapter 3: Trignometry

Summary

The Sine Law

• The sine law can be used to calculate unknown side lengths and angles in an oblique triangle.

• To use the sine law, your calculator must be in degree mode.

• The sine law can be written as $\frac{a}{\sin A}=\frac{b}{\sin {\displaystyle B}}=\frac{c}{\sin {\displaystyle C}}$or $\frac{\sin A}{a}=\frac{\sin {\displaystyle B}}{b}=\frac{\sin {\displaystyle C}}{c}$.

• To find the sine of an angle, press on your calculator.

• To find an angle, press on your calculator.

• To find an unknown side in a triangle, a matching pair and the angle opposite the side must be given. This version of the sine law should be used:
  $\frac{a}{\sin A}=\frac{b}{\sin {\displaystyle B}}=\frac{c}{\sin {\displaystyle C}}$

• To find an unknown angle is a triangle, a matching pair and the side opposite the angle must be given. This version of the sine law should be used:
  $\frac{\sin A}{a}=\frac{\sin {\displaystyle B}}{b}=\frac{\sin {\displaystyle C}}{c}$

Sum of Angles in a Triangle

If two angles are given, use the sum of the angles in a triangle, $\angle A+\angle B+\angle C=180°$, to find the third angle.