Sine Rule or Cosine Rule?
Sometimes either rule work when trying to solve for missing sides of triangles. In this example it appears we only have two pieces of information BUT because the triangle is isosceles the base angles are equal and easy to work out.
The Sine Rule seems the obvious choice here and is more straightforward BUT because AC and BC are equal we can also use the Cosine Rule, albeit with a little more algebra.
The Trigonometry section of the syllabus is the SAME (in terms of solving triangles) at Ordinary and Higher Level. To make this question trickier you have to work out the angles first and then work with tricky looking surd notation. This is just calculator work. The base of the triangle is approximately 7.65…even though it looks like something we’ve not seen before.