Sine rule

The sine rule can be used to find an angle or side if we know:

The triangle

The lengths a, b and c represent the side lengths in this triangle.
The angles A, B and C represent the angles in the triangle.

            A
          /   \
     c  /       \  b
      /           \
    /               \
   B ---------------- C
            a

Using the triangle above, the sine rule tells us that:

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

and, equivalently:

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

This means that the ratio of a side length to the sine of its opposite angle is the same for all three sides and angles in the triangle.

Question	Answer
What are the three pieces of information required to use the sine rule?	A side length, the size of the angle opposite that side, and any other side or angle.
In the triangle convention, what do the lowercase letters a, b, c represent?	The side lengths.
In the triangle convention, what do the uppercase letters A, B, C represent?	The angles.
State one form of the sine rule equation.	\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
State the other (equivalent) form of the sine rule equation.	\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}
What does the sine rule tell us about the ratio of a side length to the sine of its opposite angle?	The ratio is the same for all three sides and angles in the triangle.