Lines and planes: distances and angles

1103025301

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 6\,\mathrm{cm} \). The height of the pyramid is \( 4\,\mathrm{cm} \). Find the distance between the point \( V \) and the line \( BC \).
\( 5\,\mathrm{cm} \)
\( \sqrt{52}\,\mathrm{cm} \)
\( 25\,\mathrm{cm} \)
\( \sqrt{10}\,\mathrm{cm} \)

1103025302

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 6\,\mathrm{cm} \). The height of the pyramid is \( 4\,\mathrm{cm} \). Find the distance between the line \( S_{VB}S_{VC}\) and the line \( BC \). The points $S_{VB}$ and $S_{VC}$ are the midpoints of $VB$ and $VC$, respectively.
\( 2.5\,\mathrm{cm} \)
\( 2\,\mathrm{cm} \)
\( \frac{\sqrt{52}}2\,\mathrm{cm} \)
\( \frac{25}2\,\mathrm{cm} \)

1103025303

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 6\,\mathrm{cm} \). The height of the pyramid is \( 4\,\mathrm{cm} \). Find the distance between the line \( S_{VA}S_{VC} \) and the line \( AC \). The points $S_{VA}$ and $S_{VC}$ are the midpoints of $VA$ and $VC$, respectively.
\( 2\,\mathrm{cm} \)
\( 2.5\,\mathrm{cm} \)
\( \frac{\sqrt{52}}2\,\mathrm{cm} \)
\( 4\,\mathrm{cm} \)

1103025304

Level: 
B
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.
\( 7.5\,\mathrm{cm} \)
\( \frac23\sqrt{97}\,\mathrm{cm} \)
\( \frac{\sqrt{97}}2\,\mathrm{cm} \)
\( \sqrt{17}\,\mathrm{cm} \)

1103025305

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 4\,\mathrm{cm} \). The height of the pyramid is \( 6\,\mathrm{cm} \). Find the distance between the point \( A \) and the point \( S_{VC} \), where \( S_{VC} \) is the midpoint of the edge \( VC \).
\( 3\sqrt{3}\,\mathrm{cm} \)
\( 4\sqrt{3}\,\mathrm{cm} \)
\( \sqrt{10}\,\mathrm{cm} \)
\( 3\sqrt{10}\,\mathrm{cm} \)

1103025306

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 6\,\mathrm{cm} \). The height of the pyramid is \( 3\sqrt2\,\mathrm{cm} \). Find the distance between the point \( A \) and the line \( BV \) (see the picture).
\( 3\sqrt3\,\mathrm{cm} \)
\( 3\sqrt2\,\mathrm{cm} \)
\( \frac32\sqrt3\,\mathrm{cm} \)
\( 3\sqrt6\,\mathrm{cm} \)

2010015602

Level: 
B
The base of a pyramid is a square with the side of \(4\, \mathrm{cm}\). The height of the pyramid is \(8\, \mathrm{cm}\). Find the angle between the lateral edge of the pyramid and the base plane. Round your result to two decimal places.
\( 70.53^{\circ} \)
\( 19.47^{\circ} \)
\( 75.96^{\circ} \)

2010015603

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 12\,\mathrm{cm} \). The lateral edge of the pyramid is \( 10\,\mathrm{cm} \). Find the distance between the point \( V \) and the base \( ABCD \).
\( 8\,\mathrm{cm} \)
\( \sqrt{34}\,\mathrm{cm} \)
\( \sqrt{44}\,\mathrm{cm} \)
\( \sqrt{11}\,\mathrm{cm} \)

2010015604

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 4\,\mathrm{cm} \). The height of the pyramid is \( 6\,\mathrm{cm} \). Find the distance between the point \( A \) and the point \( S_{VB} \), where \( S_{VB} \) is the midpoint of the edge \( VB \).
\( \sqrt{19}\,\mathrm{cm} \)
\( \sqrt{35}\,\mathrm{cm} \)
\( 3\sqrt{3}\,\mathrm{cm} \)
\( \sqrt{5}\,\mathrm{cm} \)