In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $m \angle C = \theta$,then $\tan \theta = \dots$

The union of the horizontal ray and the ray of vision forms the angle of elevation; then the object under observation is $\ldots \ldots \ldots . .$

When observed from the top of a tower,the angles of depression of two houses $A$ and $B$ in the Eastern and Western directions are $30^{\circ}$ and $60^{\circ}$ respectively. Then........

The lower window of a house is at a height of $2\, m$ above the ground and its upper window is $4\, m$ vertically above the lower window. At a certain instant,the angles of elevation of a balloon from these windows are observed to be $60^{\circ}$ and $30^{\circ}$,respectively. Find the height of the balloon above the ground (in $m$).

When the angle of elevation of the sun increases from $30^{\circ}$ to $60^{\circ},$ the shadow of a tower decreases by $50\, m .$ Find the height of the tower in $m$.

$A$ tree stands vertically on the bank of a river. The angle of elevation of the top of the tree from a point exactly opposite to the tree on the other bank of the river is $60^{\circ}$. The angle of elevation of the top of the tree from a point $40 \ m$ away from that point is $30^{\circ}$. Find the width of the river and the height of the tree.