Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/6`. If side C has a length of `18` and the angle between sides B and C is `( pi)/2`, what are the lengths of sides A and B?

Answer 1

Length of side A is `36` and that of side B is `18sqrt3`.

Explanation:

It is right angled triangle, whose one of the perpendicular side C (opposite angle `pi/6`) is `18`, and hypotenuse is A. As `sin(pi/6)=1/2`, A is twice the size of C and is `36` and using Pythagoras Theorem, B will be `sqrt(36^2-18^2)` or `sqrt972` or `18sqrt3`.