Sine Rule

The sine rule is a very powerful tool used in mathematics to calculate unknown sides and angles of triangles when we only know some of the information.

For example if we have a triangle and we know two angles and one side or one angle and two sides we can calculate the rest of sides and angles of the triangle using only the sine rule and the fact that angles in a triangle add to 180 degrees. This does depend on which angles/sides we are told as we may need to use the cosine rule which we will learn in another lesson.

Example If we had a triangle ABC and we knew sides A, B and angle BC (a) we can calculate angle AC (b) using the sine rule shown below.

( sin(a) / A ) = (sin(b) / B).

We can then work about angle AB (c) using the fact the angles in a triangle add to 180.

c = ( 180 - a - b ).

We can then work out side C using the sine rule again.

( sin(c) / C ) = ( sin(b) / B ).

Now we have worked out all the information in the triangle from only three bits of information.