The tops of two poles of height $60 \ m$ and $35 \ m$ are connected by a rope. If the rope makes an angle with the horizontal whose tangent is $\frac{5}{9}$,then what is the distance (in $m$) between the two poles?

The height of a tower is $100 \text{ m}$. When the angle of elevation of the sun changes from $30^{\circ}$ to $45^{\circ}$,the shadow of the tower becomes $x \text{ m}$ smaller. The value of $x$ is (in $\text{m}$):

If $r \sin \theta = 1$ and $r \cos \theta = \sqrt{3}$,then the value of $(\sqrt{3} \tan \theta + 1)$ is

If a flagstaff of $6 \, m$ height placed on the top of a tower throws a shadow of $2 \sqrt{3} \, m$ along the ground,then the angle that the sun makes with the ground is

$A$ man standing at a point $P$ (or $L$ in the diagram) is watching the top of a tower $N$,which makes an angle of elevation of $30^{\circ}$ with the man's eye. The man walks some distance towards the tower to point $Q$ to watch its top and the angle of elevation becomes $60^{\circ}$. What is the distance (in units) between the base of the tower $M$ and the point $P$ (or $L$)?

The angle of elevation of the top of a tower from a point $20 \ m$ away from its base is $45^{\circ}$. The height of the tower is (in $m$):