From the top of a $50 \, m$ high tower,the angle of depression of a parked car is found to be $30^\circ$. Find the distance between the car and the base of the tower. (in $m$)

There is a $100\, m$ high tower at some distance from a cliff. The angle of elevation of the top of the cliff from the base of the tower is $45^{\circ}$ and the angle of depression of the base of the cliff from the top of the tower is $30^{\circ}$. Find the height of the cliff and also the distance between the tower and the cliff.

$A$ ladder is leaning against a wall such that its upper end touches the wall at a height of $3 \, m$ and the ladder is inclined at an angle of $30^{\circ}$ with the ground. Find the length of the ladder in $m$.

Write 'True' or 'False' and justify your answer.
If the height of a tower and the distance of the point of observation from its foot,both,are increased by $10 \%$,then the angle of elevation of its top remains unchanged.

The height of a tower is $30 \ m$. Find the length of the shadow of the tower,when the angle of elevation of the sun is $45^\circ$. (in $m$)

$A$ statue,$1.6 \, m$ tall,stands on the top of a pedestal. From a point on the ground,the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal.