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

If a person travels from a point $L$,towards east for $12 \ km$ and then travels $5 \ km$ towards north and reaches a point $M$,then the shortest distance from $L$ to $M$ is: (in $km$)

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

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?

$A$ person walking along a straight road towards a hill observes at two points,separated by a distance of $\sqrt{3} \text{ km}$,that the angles of elevation of the hill are $30^{\circ}$ and $60^{\circ}$. The height of the hill is

$A$ person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is $60^{\circ}$. When he moves $40 \ m$ away from the bank,he finds the angle of elevation to be $30^{\circ}$. The breadth of the river is (in $m$):