In a $\Delta ABC$,if $C = 90^{\circ}$,then $\frac{a^{2} + b^{2}}{a^{2} - b^{2}} \sin(A - B)$ is equal to:

Let $D$ be the midpoint of the side $BC$ of a triangle $ABC$. If the triangle $ADC$ is equilateral,then the ratio $a^2 : b^2 : c^2$ is equal to

In any triangle $ABC$, if $a: b: c = 2: 3: 4$, then $R: r =$

In a $\Delta ABC$,if two sides $b$ and $c$ and an angle $B$ are given.
Statement $-1$: Let $b = 5 \ cm, c = 3 \ cm$ and $\angle B = 60^\circ$. The total number of possible triangles is $2$.
Statement $-2$: If $c \sin B < b < c$ and $B$ is an acute angle,then there are two possible values of $\angle C$.

In a triangle,the lengths of the two larger sides are $10 \, cm$ and $9 \, cm$ respectively. If the angles of the triangle are in $A.P.$,then the length of the third side in $cm$ can be

Let $ABC$ be an acute-angled triangle and let $D$ be the mid-point of $BC$. If $AB = AD$,then $\tan(B) / \tan(C)$ equals