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

A house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the bottom of the first house is 60. If the distance between two houses be 6 m, then the height of the first house is

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

The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from 30$$^\circ$$ to 60$$^\circ$$ is :