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

The shadow of a tower standing on a level ground is found to be $40 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the length of the tower. (In $m$)

The upper part of a tree broken by the wind makes an angle of $30^{\circ}$ with the ground and the distance from the root to the point where the top of the tree touches the ground is $10 \ m$. What was the height of the tree?

From the top of a lighthouse,$50 \ m$ above the sea,the angle of depression of an incoming boat is $30^{\circ}$. How far is the boat from the lighthouse?

In a rectangle,if the angle between a diagonal and a side is $30^{\circ}$ and the length of the diagonal is $6 \text{ cm}$,the area (in $\text{cm}^2$) of the rectangle is:

$A$ kite is flying at a height of $75 \ m$ from the ground. The string makes an angle $\Theta$ (where $\cot \Theta = 8/15$) with the level ground. Assuming that there is no slack in the string,the length of the string is equal to (in $m$):