In a right triangle,if the measure of one of the angles is $60^{\circ}$,then the measure of the side opposite to the angle with measure $60^{\circ}$ is $\ldots \ldots$ times the measure of the hypotenuse.

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

$A$ 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 $a \sec \theta \text{ m}$.

Two ships are anchored in the opposite directions from a lighthouse. The angle of depression of one ship from the top of the lighthouse is $60^{\circ}$ and that of the other ship from the same place is found to be $30^{\circ}$. If the ship with the angle of depression of $60^{\circ}$ is $150\,m$ away from the lighthouse,find the distance between these two ships (in $m$).

$A$ pole $6\, m$ high casts a shadow $2 \sqrt{3}\, m$ long on the ground. Then,the Sun's elevation is: (in $^{\circ}$)

The union of the horizontal ray and the ray of vision forms the angle of elevation; then the object under observation is $\ldots \ldots \ldots . .$