How do you find the length of the third side of an isosceles triangle?

Using the angle (we'll call it theta) opposite the unknown side, you can find its length following this technique:

1. Draw a line from that angle to the midpoint of the unknown side, we'll call it B. This should be perpendicular to that side.

2. You have just formed two right triangles within your isosceles triangle. The hypotenuse of the right angle is your known side, we'll call it A.

3. Your angle theta has now been split in half. Calculate sin(theta/2).

4. Now you have: sin(theta/2) = (B/2)/A [Remember, sine = opposite over hypotenuse.]

5. Rearrange the equation to find B and plug in your numbers: B = 2A*sin(theta/2)