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Challenge 275: Triangle Ratios - Exactly!

It's not just 30-60 and 45-45 right-angled triangles that are special! What about a 15-75 right-angled triangle?

T is a right-angled triangle with vertices A, B, C. The angle at A is 30o and at B it is 60o. The angle at A is bisected by the line AX, where X lies on BC.

Without using a calculator, find CX:XB.

Use your work to determine the exact value of tan 15o (again without using a calculator).