Metric properties

9000120309

Level:

The sides of a rectangular box shown in the picture are

a = 3 cm

b = 4 cm

, and

c = 12 cm

. The space diagonal is

u_{t}

and the longest face diagonal is

u_{s}

. Find the ratio

u_{t} : u_{s}

13 \sqrt{10} : 40

13 : \sqrt{153}

13 : 12

4 \sqrt{10} : 5

4 \sqrt{10} : 13

9000121001

Level:

In the cube

A B C D E F G H

find the angle between the lines

A B

and

A G

{54.74}^{\circ}

60^{\circ}

{35.26}^{\circ}

{39.23}^{\circ}

9000121002

Level:

In the cube

A B C D E F G H

find the angle between the lines

C D

and

B H

{54.74}^{\circ}

60^{\circ}

{35.26}^{\circ}

{39.23}^{\circ}

9000121003

Level:

In the cube

A B C D E F G H

find the angle between the lines

B S_{D H}

and

A E

, where the point

S_{D H}

is the center of the edge

D H

{70.53}^{\circ}

{29.47}^{\circ}

{35.26}^{\circ}

{54.74}^{\circ}

9000121004

Level:

In the cube

A B C D E F G H

find the angle between the lines

S_{A E} S_{H C}

and

S_{H C} S_{B F}

, where

S_{A E}

S_{H C}

and

S_{B F}

are the centers of the segments

A E

H C

and

B F

, respectively.

{53.13}^{\circ}

{26.57}^{\circ}

60^{\circ}

{36.87}^{\circ}

9000121005

Level:

In the cube

A B C D E F G H

find the angle between the lines

A S_{B C}

and

A D

, where

S_{B C}

is the center of the edge

B C

{63.43}^{\circ}

{26.57}^{\circ}

{53.13}^{\circ}

{36.87}^{\circ}

9000121006

Level:

In the cube

A B C D E F G H

find the angle between the lines

B G

and

G D

60^{\circ}

45^{\circ}

{36.87}^{\circ}

{53.13}^{\circ}

9000121007

Level:

In the cube

A B C D E F G H

find the angle between the lines

S_{B E} S_{A H}

and

H C

, where

S_{B E}

and

S_{A H}

are centers of the segments

B E

and

A H

, respectively.

60^{\circ}

{26.57}^{\circ}

45^{\circ}

{53.13}^{\circ}

9000121008

Level:

In the cube

A B C D E F G H

find the angle between the lines

D B

and

A G

90^{\circ}

45^{\circ}

{35.26}^{\circ}

{53.13}^{\circ}

9000121009

Level:

In the cube

A B C D E F G H

find the angle between the lines

S_{H D} S_{F C}

and

A B

, where the points

S_{H D}

and

S_{F C}

are centers of

H D

and

F C

, respectively.

{26.57}^{\circ}

45^{\circ}

{54.74}^{\circ}

60^{\circ}

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9000120309

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