As observed from the top of a building,the angle of depression of a man standing $10 \, m$ away from the building is found to be $45^{\circ}$. Find the height of the building (in $m$).

As observed from a hill $340 \ m$ high,the angles of depression of two houses situated to the east and west of the hill are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the distance between the two houses. (in $m$)

$A$ kite is flying at a height of $60\, m$ above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$. Find the length of the string,assuming that there is no slack in the string.

An erect tree is $300\, m$ away from a hill. If the height of the hill is $300\, m$,find the angle of depression of the base of the tree from the top of the hill. (in $^{\circ}$)

$A$ flag-staff stands on the top of a building. The angle of elevation of the top of the building is $45^{\circ}$ and that of the top of the flag-staff is $60^{\circ}$,as observed by a man standing $15\, m$ away from the building. Find the height of the flag-staff from the top of the building (in $m$).

From the top of a $7 \,m$ high building,the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.