The angle of elevation of the top of a tower from a point $20 \ m$ away from its base is $45^{\circ}$. The height of the tower is (in $m$):

The angle of elevation of a tower from a distance $50 \; m$ from its foot is $30^{\circ}$. The height of the tower is

$A$ pole is broken by the wind. The top of the pole strikes the ground at an angle of $30^{\circ}$ and at a distance of $21 \ m$ from the foot of the pole. Find the total height of the pole (in $m$).

The angles of elevation of the top of a tower from the points $P$ and $Q,$ at distances of $a$ and $b$ respectively from the base of the tower and in the same straight line with it,are complementary. The height of the tower is

The shadow of a tower standing on a level plane is found to be $50 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ Find the height of the tower. (In $m$)

The angle of elevation of a ladder leaning against a wall is $45^{\circ},$ and the foot of the ladder is $4.242 \ m$ away from the wall. The length of the ladder is (in $m$):