Lines and planes: distances and angles

1103018801

Level: 
A
Choose the correct verbal description of the angle shown in the picture:
The angle between two space diagonals of a cube.
The angle between a space diagonal of a cube and its edge.
The angle between two face diagonals of a cube.
The angle between a space diagonal of a cube and a face diagonal.

1103018802

Level: 
A
Choose the correct verbal description of the angle shown in the picture.
The angle between a space diagonal of a cube and its face diagonal.
The angle between a space diagonal of a cube and its edge.
The angle between two face diagonals of a cube.
The angle between a face diagonal of a cube and its edge.

1103018804

Level: 
A
Choose the correct verbal description of the angle shown in the picture, where the point \(S_{EF}\) is the midpoint of the edge \(EF\).
The angle between the line \(AS_{EF}\) and the plane \(BCG\) (right side face).
The angle between the line \(AS_{EF}\) and the plane \(EFG\) (top face).
The angle between the line \(AS_{EF}\) and the plane \(DCG\) (back face).
The angle between the line \(AS_{EF}\) and the plane \(ABF\) (front face).

1103018902

Level: 
A
Let \( \varphi \) bet the angle between a space diagonal of a cube and its face diagonal. Choose the correct expression for \( \varphi \).
\( \mathrm{tg}\,\varphi = \frac{\sqrt2}2 \)
\( \mathrm{sin}\,\varphi = \frac{\sqrt2}2 \)
\( \mathrm{tg}\,\varphi = \frac{\sqrt3}3 \)
\( \mathrm{tg}\,\varphi = \frac{\sqrt6}3 \)

1103018903

Level: 
A
In the cube \( ABCDEFGH \) with \( S_{AC} \) being the midpoint of the diagonal \( AC \), let \( \varphi \) be the angle between the line \( ES_{AC} \) and the bottom face \( ABCD \). Choose the correct expression for \( \varphi \).
\( \mathrm{tg}\,\varphi = \sqrt2 \)
\( \mathrm{sin}\,\varphi = \frac{\sqrt2}3 \)
\( \mathrm{tg}\,\varphi = \frac{\sqrt2}2 \)
\( \mathrm{cos}\,\varphi = \frac{\sqrt6}3 \)

1103018905

Level: 
A
In the cube \( ABCDEFGH \) with \( S_{AC} \) being the midpoint of the diagonal \( AC \), let \( \varphi \) be the angle between the line \( EG \) and the line \( GS_{AC} \). Choose the correct expression for \( \varphi \):
\( \mathrm{tg}\,\varphi = \sqrt2 \)
\( \mathrm{sin}\,\varphi = \frac{\sqrt3}3 \)
\( \mathrm{tg}\,\varphi = \frac{\sqrt2}2 \)
\( \mathrm{cos}\,\varphi = \frac{\sqrt6}3 \)