Metric properties

In the cube $ABCDEFGH$, let $S_{FG}$ be the midpoint of the edge $FG$. Find the angle between the lines $B{S}_{FG}$ and $BF$. Round the result to two decimal places.

Let $\phi$ bet the angle between a space diagonal of a cube and its face diagonal. Choose the correct expression for $\phi$.

The base $ABCD$ of a square pyramid $ABCDV$ has an edge of $6\mathrm{cm}$. The height of the pyramid is $3\sqrt{2}\mathrm{cm}$. Find the distance between the point $A$ and the line $BV$ (see the picture).

The base $ABCD$ of a square pyramid $ABCDV$ has an edge of $8\mathrm{cm}$. The height of the pyramid is $9\mathrm{cm}$. Find the distance between the line $S_{VA}{S}_{VD}$ and the line $BC$. The points $S_{VA}$ and $S_{VD}$ are the midpoints of $VA$ and $VD$, respectively.