The greatest angle of the triangle whose sides are $x^2+x+1$,$2x+1$,and $x^2-1$ is (in $^{\circ}$)

In triangle $ABC$,$\frac{\tan A}{2} = \frac{\tan B}{3} = \frac{\tan C}{4}$,then the value of $\sec^2 A + \sec^2 B + \sec^2 C$ is:

In $\triangle ABC$,if $\sin^2 A + \sin^2 B = \sin^2 C$ and $l(AB) = 10$,then the maximum value of the area of $\triangle ABC$ is

The sum of solutions of the equation $\frac{\cos x}{1+\sin x}=|\tan 2 x|$,where $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) - \left\{\frac{\pi}{4}, -\frac{\pi}{4}\right\}$,is:

$ABC$ is a triangular park with $AB = AC = 100 \, m$. $A$ clock tower is situated at the mid-point $D$ of $BC$. The angles of elevation of the top of the tower at $A$ and $B$ are $\cot^{-1} 3.2$ and $\csc^{-1} 2.6$ respectively. The height of the tower is .... $m$.

Let $p_1, p_2, p_3$ be the altitudes of a triangle $ABC$ drawn through the vertices $A, B, C$ respectively. If $r_1=4, r_2=6, r_3=12$ are the ex-radii of triangle $ABC$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$