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 $m$)

Two cars are parked in the same direction of a tower. Observing from the top of the tower,their angles of depression are found to be $60^{\circ}$ and $30^{\circ}$. If the car nearer to the tower is $75\, m$ away from the tower,find the distance between these two cars (in $m$).

The angle of elevation of the top of a tower from a certain point is $30^{\circ}$. If the observer moves $20 \, m$ towards the tower,the angle of elevation of the top increases by $15^{\circ}$. Find the height of the tower.

From the top of a hill $100 \, m$ high,the angles of depression of the top and the bottom of a tower are observed to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the height of the tower in meters.

The angle of elevation of the top of a hill from a point on the ground is $30^\circ$. After walking $30 \, m$ towards the hill,the angle of elevation becomes $45^\circ$. What is the height of the hill? (in $m$)

The angle of depression of the base of a tower from the top of a cliff is $60^{\circ}$ and the angle of elevation of the top of the tower from the base of the cliff is $30^{\circ}$. If the height of the tower is $50 \, m$,find the height of the cliff in meters.