Lines and planes: distances and angles

1103056006

Level: 
A
The cube \( ABCDEFGH \) shown in the picture has edges of length \( a=6\,\mathrm{cm} \). Find the distance between the point \( B \) and the line \( EG \).
\( 3\sqrt6\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)
\( 3\sqrt5\,\mathrm{cm} \)
\( \frac{3\sqrt6}2\,\mathrm{cm} \)

1103061401

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the plane \( EFB \) and the plane \( HGB \) (see the picture). Round the result to two decimal places.
\( 26.57^{\circ} \)
\( 45^{\circ} \)
\( 22.5^{\circ} \)
\( 31.43^{\circ} \)

1103061402

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( AC \) and \( SC \), where \( S \) is the midpoint of the diagonal \( EG \) (see the picture). Round the result to two decimal places.
\( 65.74^{\circ} \)
\( 70.28^{\circ} \)
\( 75^{\circ} \)
\( 45^{\circ} \)

1103061403

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( CG \) and \( SC \), where \( S \) is the midpoint of the diagonal \( EG \) (see the picture). Round the result to two decimal places.
\( 24.26^{\circ} \)
\( 45^{\circ} \)
\( 35.24^{\circ} \)
\( 63.21^{\circ} \)

1103061404

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( HG \) and \( AH \) (see the picture). Round the result to two decimal places.
\( 90^{\circ} \)
\( 85^{\circ} \)
\( 56.15^{\circ} \)
\( 33.85^{\circ} \)

1103061405

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( AG \) and \( BH \) (see the picture). Round the result to two decimal places.
\( 67.71^{\circ} \)
\( 45^{\circ} \)
\( 37.08^{\circ} \)
\( 49.1^{\circ} \)

1103061406

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the planes \( ABC \) and \( EFC \) (see the picture). Round the result to two decimal places.
\( 63.43^{\circ} \)
\( 26.57^{\circ} \)
\( 45^{\circ} \)
\( 56.2^{\circ} \)

1103061407

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( CG \) and \( EC \) (see the picture). Round the result to two decimal places.
\( 42.03^{\circ} \)
\( 47.97^{\circ} \)
\( 45^{\circ} \)
\( 50.04^{\circ} \)