The angles of a triangle are in the ratio $1: 2: 7$. The ratio of the greatest side to the least side is $(k+1):(k-1)$. The value of $k$ is

Let $A, B$ and $C$ be the angles of a triangle and $\tan \frac{A}{2}=\frac{2}{5}, \tan \frac{B}{2}=\frac{3}{7}$. Then, $\tan \frac{C}{2}$ is equal to

Let $ A, B $ and $ C $ are the angles of a triangle and $ \tan \frac{A}{2}=\frac{1}{3}, \tan \frac{B}{2}=\frac{2}{3} $. Then, $ \tan \frac{C}{2} $ is equal to

$ A B C $ is a triangular park with $ A B=A C=100 \mathrm{~m} $. A TV tower stands at the mid-point of $ B C $. The angles of elevation of the top of the tower at $ A $, $ B, C $ are $ 45^{\circ}, 60^{\circ}, 60^{\circ} $ respectively. The height of the tower is