$A$ balloon is descending at a rate of $4 \, m/min$. Its angle of elevation from a point on the ground is $45^\circ$,which reduces to $30^\circ$ after $10 \, minutes$. At what distance from the observer will the balloon touch the ground?

From the top of a lighthouse $30 \ m$ high with its base at sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be $45^o$ from a point $A$ on the plane. Let $B$ be a point $30 \, m$ vertically above the point $A$. If the angle of elevation of the top of the tower from $B$ is $30^o$,then the distance (in $m$) of the foot of the tower from the point $A$ is:

The angle of elevation of the top of a mobile tower from three points $P, Q$ and $R$ (on a straight line through the foot of the tower) are $\alpha, \beta$ and $\gamma$ respectively. If all three points lie on the same side of the foot of the tower and $\alpha : \beta : \gamma = 1 : 2 : 3$ and $PQ = l$,then the height of the tower is -

Consider a triangular plot $ABC$ with sides $AB = 7 \ m$,$BC = 5 \ m$,and $CA = 6 \ m$. $A$ vertical lamp-post at the midpoint $D$ of $AC$ subtends an angle $30^o$ at $B$. The height (in $m$) of the lamp-post is

$A$ vertical pole fixed to the horizontal ground is divided in the ratio $3:7$ by a mark on it,with the lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground $18 \ m$ away from the base of the pole,then the height of the pole (in $meters$) is: