Consider a cube *ABCDEFGH*, |*AB*|* = a = *4 cm. Find the distance from a point *F* to a given straight line :

Consider a cuboid *ABCDEFGH*, |*AB*|* = a = *60 cm, |*AD*|* = b = *400 mm, |*AE*|* = c = *8 dm. Find the distance from a point *B* to a point *H*, distance from a point *D* to a point *G* and the distance from a point *C* to a point *F*.

Consider a cone with a base diameter of *d = *12 cm. Any point on the circumference of the base is located 8.5 cm from the apex of the cone. Find the distance from the apex *V* to the base.

Consider a truncated pyramid *ABCDEFGH* with square bases. Find the distance between planes *ABCD* and *EFGH*, if you know |*AC*|* = *13 cm, |*FH*|* = *9 cm and |*AG*|* = *15 cm.

Consider a triangular prism *ABCDEF* with a base of right triangle, which has the right angles at the vertices *C* and *F*. The lengths of legs are |*AC*|* = *8 m, |*BC*|* = *6 m and a height of the prism is *h = *15 m. Find the distance between points *E* and *S* and the size of an angle *φ* = |∠*BSE*|, where *S* is the midpoint of an edge *AC*.

Consider a cube *ABCDEFGH* with the points on its edges *X*∈*EH*, *Y*∈*AB*, *Z*∈*GH*, if we know |*EH*|* = *|*XH*|, |*AY*|* = *|*YB*|, |*ZH*|* = *3|*GZ*|. Find the angle between the straight lines *AX* and *YZ*.

Consider a cube *ABCDEFGH*. Let *M* be a midpoint of an edge *AE* and the size of a cube's edge is *a*. Find the angle between the straight lines *BH* and *BM*.

Consider a regular square pyramid *ABCDV*, |*AB*|* = a*, |*AV*|* = a*. Find the angle between two adjacent slant faces of the pyramid.

Consider a cube *ABCDEFGH*. Find the angle between the planes *ABC* and *ACF*.

Consider a regular hexagonal pyramid *ABCDEFV*, where |*AB*|* = a*, |*AV*|* = *2*a* and a point *M* is the midpoint of the edge *AV*. Find the distance from the point *M* to the straight line *DV*.

Consider a cuboid *ABCDEFGH*. Find the distance from the straight line *AC* to the straight line *FH* and the volume of a cuboid, if |*AG*|* = *5, |*AC*|* = *3, |*AH*|* = *.

Consider a cube *ABCDEFGH*, where |*AB*|* = a = *5 cm, point *M* is the midpoint of the edge *EF*, point *K* is the midpoint of the edge *CD*. Find the distance from the plane *BMG* to the plane *HAK*.

Consider a regular square pyramid *ABCDV*, where |*AB*|* = a = *4 cm, |*AV*|* = b = *6 cm. Find the angle between two planes *BCV* and *ABC*.

Consider a cube *ABCDEFGH*, let a point *K* be the midpoint of the edge *FG*. Find out whether the planes *ADK* and *DCH* are perpendicular to each other.

Consider a regular tetrahedron *ABCD*, |*AB*|* = a*. Find the distance between two straight lines on which lie opposite edges of the tetrahedron.

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