Lines and planes: distances and angles

1103107012

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the plane \( ADD' \) and the plane \( CDD' \) (see the picture).
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 90^{\circ} \)
\( 72^{\circ} \)

1103107013

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the plane \( BCC' \) and the plane \( CDD' \) (see the picture).
\( 60^{\circ} \)
\( 120^{\circ} \)
\( 90^{\circ} \)
\( 72^{\circ} \)

1103107014

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the line \( BA’ \) and the plane \( AEE’ \) (see the picture). Round the result to two decimal places.
\( 26.57^{\circ} \)
\( 63.43^{\circ} \)
\( 30^{\circ} \)
\( 22.5^{\circ} \)

2010015601

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the side \( a \) of the length \( 3\,\mathrm{cm} \) and the height \( v \) of the length \( 8\,\mathrm{cm} \). Find the angle between the lines \( AD' \) and \( CD' \). Round the result to two decimal places.
\( 31.31^{\circ} \)
\( 58.69^{\circ} \)
\( 16.70^{\circ} \)
\( 20.57^{\circ} \)

2010015801

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 6\,\mathrm{cm} \). Find the distance between the lines \( FA \) and \( D'C' \) (see the picture).
\( 2\sqrt{21}\,\mathrm{cm} \)
\( 4\sqrt{3}\,\mathrm{cm} \)
\( 10\,\mathrm{cm} \)
\( 2\sqrt{13}\,\mathrm{cm} \)

2010015802

Level: 
C
Let \( ABCDEFV \) be a regular hexagonal pyramid with a base edge length of \( 4\,\mathrm{cm} \) and a height of \( 8\,\mathrm{cm} \). Find the distance between the point \( V \) and the line \( BD \) (see the picture).
\( 2\sqrt{17}\,\mathrm{cm} \)
\( 4\sqrt{3}\,\mathrm{cm} \)
\( 2\sqrt{19}\,\mathrm{cm} \)
\( 2\sqrt{20}\,\mathrm{cm} \)

2010015806

Level: 
C
The side of a regular hexagonal prism \(ABCDEFA'B'C'D'E'F'\) shown in the picture is \(a = 3\, \mathrm{cm}\) and the height is \(v = 8\, \mathrm{cm}\). Find the angle between the diagonal \(AC'\) and the base plane \(ABC\) (round your result to the nearest degree).
\(57^{\circ }\)
\(53^{\circ }\)
\(33^{\circ }\)
\(38^{\circ }\)

9000120304

Level: 
C
The side of a regular hexagonal prism \(ABCDEFA'B'C'D'E'F'\) is \(a = 3\, \mathrm{cm}\) and the height \(v = 8\, \mathrm{cm}\). Find the length of the diagonal \(AD'\).
\(10\, \mathrm{cm}\)
\(\sqrt{73}\, \mathrm{cm}\)
\(\sqrt{82}\, \mathrm{cm}\)
\(2\sqrt{8}\, \mathrm{cm}\)
\(2\sqrt{6}\, \mathrm{cm}\)

9000120305

Level: 
C
The side of a regular hexagonal prism \(ABCDEFA'B'C'D'E'F'\) shown in the picture is \(a = 3\, \mathrm{cm}\) and the height is \(v = 8\, \mathrm{cm}\). Find the angle between the diagonal \(AD'\) and the base plane \(ABC\) (round your result to the nearest degree).
\(53^{\circ }\)
\(37^{\circ }\)
\(45^{\circ }\)
\(61^{\circ }\)
\(72^{\circ }\)