Sine & cosine rules
SOH CAH TOA only works in right-angled triangles — but the world is full of triangles that have no right angle at all. In this lesson we meet the two rules that handle any triangle: the sine rule and the cosine rule. We learn to name a triangle properly, use the sine rule to find a side and an angle, use the cosine rule to find a side and an angle, work out the area with ½ ab sin C, and — most importantly — decide which rule to reach for from the information we are given. We finish with a real bearings problem where two ships sail off in different directions and we find the distance between them.
By the end you should be able to (NSSCO Mathematics 11.3):
- Name the sides and angles of any triangle, so that side a is opposite angle A, side b opposite B and side c opposite C
- Use the sine rule a/sinA = b/sinB = c/sinC to find an unknown side
- Use the sine rule to find an unknown angle
- Use the cosine rule a² = b² + c² − 2bc·cosA to find an unknown side
- Rearrange the cosine rule to cosA = (b² + c² − a²) / (2bc) to find an unknown angle
- Find the area of a triangle using ½ ab sin C
- Choose the correct rule from the information given in a problem
- Solve real problems, including bearings, using non-right-angled triangles
Miss Jay Jay and Mike talk through the whole topic — with the figure and working drawn live.