The angle of elevation of the top of a tower from a point on the ground,which is $30\, m$ away from the foot of the tower,is $30^{\circ}$. Find the height of the tower.

$A$ circus artist is climbing a $20\, m$ long rope,which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole,if the angle made by the rope with the ground level is $30^{\circ}$ (see figure). (in $m$)

The angle of elevation of the top of a building from the foot of the tower is $30^{\circ}$ and the angle of elevation of the top of the tower from the foot of the building is $60^{\circ}$. If the tower is $50\, m$ high,find the height of the building.

An electrician has to repair an electric fault on a pole of height $5\, m$. She needs to reach a point $1.3\, m$ below the top of the pole to undertake the repair work (see figure). What should be the length of the ladder that she should use which,when inclined at an angle of $60^{\circ}$ to the horizontal,would enable her to reach the required position? Also,how far from the foot of the pole should she place the foot of the ladder? (You may take $\sqrt{3}=1.73$)

An observer $1.5\, m$ tall is $28.5\, m$ away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^{\circ}$. What is the height of the chimney? (in $m$)

From a point $P$ on the ground,the angle of elevation of the top of a $10 \, m$ tall building is $30^{\circ}$. $A$ flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from $P$ is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point $P$. (You may take $\sqrt{3} = 1.732$)