The trigonometric ratios sine, cosine and tangent are used to calculate angles and sides in right angled triangles. We are now going to extend trigonometry beyond right angled triangles and use it to solve problems involving any triangle.
We can use the sine rule when we're given the sizes of:
Find the size of angle R.
Substitute the information from the diagram
Use 'change side, change operation'.
Moving sin to the other side becomes sin-1.
Remember to press 'shift' then 'sin' to get 'sin-1' on your calculator.
Now try the example question below.
Find the length of YZ.
We know two angles and so the third angle in the triangle must make up the total ie .