Two boats are anchored in the same direction from a $100 \, m$ high lighthouse. The angles of depression of the boats from the top of the lighthouse are $30^{\circ}$ and $45^{\circ}$. Find the distance between these two boats (in $m$).

There is a slope making an angle of measure $30^{\circ}$ with the ground level. $A$ man walks on the slope for $x \, m$ and reaches a point at a height of $y \, m$ from the ground. Then,which of the following holds true?

$A$ cable tied to the top of an electric pole is affixed at a point on the ground $a \text{ m}$ away from the pole. If the cable makes an angle $\theta$ with the ground,then prove that the height of the pole is $a \tan \theta \text{ m}$ and the length of the wire is $a \sec \theta \text{ m}$.

The approximate value of $\frac{1}{\sqrt{3}}$ up to $2$ decimal places is.........

The shadow of a tower standing on a level plane is found to be $50 \, m$ longer when the Sun's elevation is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower (in $m$).

$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $22\, m$ and it makes an angle of measure $30^{\circ}$ with the ground. Find the height of the electric pole (in $m$).