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?

When the length of the shadow of a pole is equal to the height of the pole,then the angle of elevation of the source of light is: (in $^{\circ}$)

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 $m$):

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 angle of elevation of the sun,when the length of the shadow of a tree is $\sqrt{3}$ times the height of the tree,is (in $^{\circ}$)

From a point $P$ on the ground,the angle of elevation of the top of a $10 \ m$ tall building is $30^{\circ}$. $A$ flag is hoisted at the top of the building,and the angle of elevation of the top of the flagstaff from $P$ is $45^{\circ}$. Find the length of the flagstaff. (Take $\sqrt{3} = 1.732$) (In $m$)