The angles of depressions from the top of a pole located at the centre of a square, at the vertex and the midpoint of a side of the square are $\mathrm{\alpha }$ and $\mathrm{\beta }$ respectively. Then

Two poles of the height $12 m$ and $17 m$ stand vertically upright on a plain ground. If the distance between their feet is $12 m$, find the distance between their tops.

A sphere with centre $O$ sits atop a pole as shown in the figure. An observer on the ground is at a distance $50 m$ from the foot of the pole. She notes that the angles of elevation from the observer to points $P$ and $Q$ on the sphere are $30°$ and $60°$ , respectively. Then, the radius of the sphere in meters is

A ladder $10 m$ long is leaning against a vertical wall. It makes an angle of $60°$ with the ground. How far is the foot of the ladder from the wall?

X is $5 m$ tall and he notices that he casts a shadow that is $3 m$ long. He then measures that the shadow cast by his school building is $30 m$ long. How tall is the building?