The Sine Law
This lesson looks at the development and preliminary applications of the Sine Law. The video lesson first works through the development of the algebraic proof for the Sine Law. This requires the prior understandings of the primary trigonometric ratio of Sine. This sine law is used on non-right angle triangles to solve for unknown angles or sides. The overlaying idea of how this sine law is derived is that we are cutting the triangle into two right angle triangles and using the sine ratio to solve for 2 of the three sides. We do this again to solve for a third side. This shows that all three ratios of sides lengths divided by the ratio of sine for the corresponding angle (to the side length) are equal to each other.
Through the investigative proof we found applying this ratio to be true.
Therefore, we are able to use the following ratio to solve for unknown angles and sides of non-right angle triangles.
A quick summary of what information you need given in a problem to be able to solve for which known is shown below:
- The sine law can be used to find a side length of a non-right triangle if given two angles and one side length.
- The sine law can be used to find an angle of a non-right triangle if given two sides and one angle that is corresponds to one of the given sides (i.e., the angle cannot be contained by the given sides)
Follow the link below for the video of this lesson
8.1 - Trigonometry - The Law of Sines
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