## Challenge 275: Triangle Ratios - Exactly!

T is a right-angled triangle with vertices A, B, C. The angle at A is 30^{o} and at B it is 60^{o}. 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 15^{o} (again without using a calculator).