Some Applications of Trigonometry question bank (Maths)

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 and the distance of the building from the point $P$. (You may take $\sqrt{3} = 1.732$)

The angles of depression of the top and the bottom of an $8 \, m$ tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$,respectively. Find the height of the multi-storeyed building and the distance between the two buildings.