Let $$\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}$$, where $$A, B$$ and $$C$$ are angles of a $$\triangle A B C$$. If the lengths of the sides opposite these angles are $$a, b$$ and $$c$$ respectively, then

Let $$\alpha$$ be the solution of $${16^{{{\sin }^2}\theta }} + {16^{{{\cos }^2}\theta }} = 10$$ in $$\left( {0,{\pi \over 4}} \right)$$. If the shadow of a vertical pole is $${1 \over {\sqrt 3 }}$$ of its height, then the altitude of the sun is

Given that a house forms a right angle view from a window of another house, and the angle of elevation from the base of the first house to the window is 60 degrees. If the separation between the two houses is 6 meters, calculate the height of the first house.

If in a $$\Delta$$ABC, 2b^{2} = a^{2} + c^{2}, then $$\frac{\sin 3B}{\sin B}$$ is equal to