Metric properties

9000121010

Level:

In the cube

A B C D E F G H

find the angle between the lines

E S_{C G}

and

A G

, where

S_{C G}

is the center of the

C G

{54.74}^{\circ}

{19.47}^{\circ}

{35.26}^{\circ}

60^{\circ}

1103025301

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

6 cm

. The height of the pyramid is

4 cm

. Find the distance between the point

V

and the line

B C

5 cm

\sqrt{52} cm

25 cm

\sqrt{10} cm

1103025302

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

6 cm

. The height of the pyramid is

4 cm

. Find the distance between the line

S_{V B} S_{V C}

and the line

B C

. The points

S_{V B}

and

S_{V C}

are the midpoints of

V B

and

V C

, respectively.

2.5 cm

2 cm

\frac{\sqrt{52}}{2} cm

\frac{25}{2} cm

1103025303

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

6 cm

. The height of the pyramid is

4 cm

. Find the distance between the line

S_{V A} S_{V C}

and the line

A C

. The points

S_{V A}

and

S_{V C}

are the midpoints of

V A

and

V C

, respectively.

2 cm

2.5 cm

\frac{\sqrt{52}}{2} cm

4 cm

1103025304

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

8 cm

. The height of the pyramid is

9 cm

. Find the distance between the line

S_{V A} S_{V D}

and the line

B C

. The points

S_{V A}

and

S_{V D}

are the midpoints of

V A

and

V D

, respectively.

7.5 cm

\frac{2}{3} \sqrt{97} cm

\frac{\sqrt{97}}{2} cm

\sqrt{17} cm

1103025305

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

4 cm

. The height of the pyramid is

6 cm

. Find the distance between the point

A

and the point

S_{V C}

, where

S_{V C}

is the midpoint of the edge

V C

3 \sqrt{3} cm

4 \sqrt{3} cm

\sqrt{10} cm

3 \sqrt{10} cm

1103025306

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

6 cm

. The height of the pyramid is

3 \sqrt{2} cm

. Find the distance between the point

A

and the line

B V

(see the picture).

3 \sqrt{3} cm

3 \sqrt{2} cm

\frac{3}{2} \sqrt{3} cm

3 \sqrt{6} cm

2010015602

Level:

The base of a pyramid is a square with the side of

4 cm

. The height of the pyramid is

8 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:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

12 cm

. The lateral edge of the pyramid is

10 cm

. Find the distance between the point

V

and the base

A B C D

8 cm

\sqrt{34} cm

\sqrt{44} cm

\sqrt{11} cm

2010015604

Level:

The base

A B C D

of a square pyramid

A B C D V

has an edge of

4 cm

. The height of the pyramid is

6 cm

. Find the distance between the point

A

and the point

S_{V B}

, where

S_{V B}

is the midpoint of the edge

V B

\sqrt{19} cm

\sqrt{35} cm

3 \sqrt{3} cm

\sqrt{5} cm

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9000121010

1103025301

1103025302

1103025303

1103025304

1103025305

1103025306

2010015602

2010015603

2010015604

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