However, if we wanted to solve for the last side, how would we do it?
We cannot use Pythagorean theorem, because this is not a right-angled triangle.
We also cannot use any of the trigonometric identities we have studied so far, because those trig ratios only apply when there is a right-angled triangle.
Luckily, mathematicians discovered this "problem", and came up with yet another method to use in order to find missing sides and angles in non-right angled triangles.
One of the methods they discovered is called The Sine Law.
The Sine Law is as follows:
The top version of the sine law is what you should use when you are finding a missing angle. The bottom version of the sine law is what you should use when you are finding a missing side length. It doesn't really matter which variation you use, but if you follow those guidelines, it will be much easier to solve the problem.
For the mathematical proof of the Sine Law, see page 552 of the text.
When can I use the sine law?
One of the following conditions must be met:
a) two sides and one angle across from a known side are known or
b) two angles and any side are known
Example 1: Find the missing side length in the following triangle.
This time, because we are finding an angle instead of a side, we will need to use the top variation of the Sine Law.
Practice Questions
Page 556 #6,7,9,10,12
