$A$ ladder $15 \, m$ long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall,find the height of the wall in $m$.

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

From the top of a $70\, m$ tall tower,the angle of depression of the top and the base of a pole are found to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the pole from the tower and the height of the pole.

$A$ ladder leans on a wall to reach a height of $3 \, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........... $m$.

The angle of depression of the top of a building from the top of a tower is $45^{\circ}$ and that of the base of the building from the top of the tower is $60^{\circ}$. If the height of the building is $7 \, m$,find the height of the tower.

$A$ pole stands on the ground. Watching from the top of the pole,the angle of depression of a stone on the ground $10 \, m$ away from the pole is $60^{\circ}$. Then the height of the pole is $\ldots \ldots \ldots \, m$. (Take $\sqrt{3} = 1.73$.)