Trigonometry Questions

The sum of the radii of inscribed and circumscribed circles for an $n$ -sided regular polygon of side $a$, is:

If in a triangle $ABC$, $a{\cos }^2\left(\frac{C}{2}\right)+c{\cos }^2\left(\frac{A}{2}\right)=\frac{3b}{2}$, then the sides $a,b$ and $c$:

The upper $\frac{3}{4}$ th portion of a vertical pole subtends an angle ${\tan }^{-1}\frac{3}{5}$ at point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is: