In $\Delta ABC$,$AB = AC$ and $\angle C = 75^{\circ}$,then find $\angle B$. (in $^{\circ}$)

$D$ is a point on the side $BC$ of a $\triangle ABC$ such that $AD$ bisects $\angle BAC$. Then

In $\Delta ABC$,$AB = 6 \, cm$,$BC = 8 \, cm$,and $AC = 10 \, cm$. $BM$ is an altitude on $AC$. Then $BM = \dots \, cm$.

In $\triangle PQR$,$\angle P = 70^{\circ}$ and $\angle R = 30^{\circ}$. Which side of this triangle is the longest? Give a reason for your answer.

The angles of a triangle are in the ratio $5:3:7$. The triangle is

For an equilateral triangle,each of whose side is $a$,the length of any altitude of that triangle is ...........