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?

When the sun is $30^{\circ}$ above the horizontal,the length (in $m$) of the shadow cast by a building $50 \ m$ high is

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 $m$):

The expression $\frac{\sin A}{1+\cos A}+\frac{\sin A}{1-\cos A}$ is equal to:

The angle of elevation of an aeroplane from a point on the ground is $60^{\circ}$. After flying for $30$ seconds, the angle of elevation changes to $30^{\circ}$. If the aeroplane is flying at a constant height of $4500 \text{ m}$, what is the speed (in $\text{m/s}$) of the aeroplane (in $\sqrt{3}$)?

The angle of elevation of the top of a tower at a point $G$ on the ground is $30^{\circ}$. On walking $20 \ m$ towards the tower,the angle of elevation becomes $60^{\circ}$. The height of the tower is equal to