$A$ man having height $169 \; cm$ is standing near a pole. He casts a shadow $130 \; cm$ long. What is the length (in $cm$) of the pole if it casts a shadow $420 \; cm$ long?

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 $m$)

The angle of elevation of the sun when the length of the shadow of a pole is $\sqrt{3}$ times the height of the pole will be (in $^{\circ}$)

$A$ tower subtends an angle of $30^{\circ}$ at a point on the same level as the foot of the tower. At a second point,$h \ m$ above the first,the angle of depression of the foot of the tower is $60^{\circ}$. The horizontal distance of the tower from the point is

The angle of elevation of a tower from a distance of $100 \ m$ from its foot is $30^{\circ}$. Then the height of the tower is (in $m$):

The angles of depression from the top of a lighthouse to two boats,which are $60 \, m$ apart and in the same direction (due east),are $45^{\circ}$ and $30^{\circ}$. The height of the lighthouse is: