Metric properties

1103061404

Level:

The rectangular box

A B C D E F G H

has sides of lengths

| A B | = 6 cm

| B C | = 4 cm

| A E | = 8 cm

. Find the angle between the lines

H G

and

A H

(see the picture). Round the result to two decimal places.

90^{\circ}

85^{\circ}

{56.15}^{\circ}

{33.85}^{\circ}

1103061403

Level:

The rectangular box

A B C D E F G H

has sides of lengths

| A B | = 6 cm

| B C | = 4 cm

| A E | = 8 cm

. Find the angle between the lines

C G

and

S C

, where

S

is the midpoint of the diagonal

E G

(see the picture). Round the result to two decimal places.

{24.26}^{\circ}

45^{\circ}

{35.24}^{\circ}

{63.21}^{\circ}

1103061402

Level:

The rectangular box

A B C D E F G H

has sides of lengths

| A B | = 6 cm

| B C | = 4 cm

| A E | = 8 cm

. Find the angle between the lines

A C

and

S C

, where

S

is the midpoint of the diagonal

E G

(see the picture). Round the result to two decimal places.

{65.74}^{\circ}

{70.28}^{\circ}

75^{\circ}

45^{\circ}

1103061401

Level:

The rectangular box

A B C D E F G H

has sides of lengths

| A B | = 6 cm

| B C | = 4 cm

| A E | = 8 cm

. Find the angle between the plane

E F B

and the plane

H G B

(see the picture). Round the result to two decimal places.

{26.57}^{\circ}

45^{\circ}

{22.5}^{\circ}

{31.43}^{\circ}

1103101209

Level:

Let

A B C D

be a regular tetrahedron with an edge length of

3 cm

. Find the height

| D T |

of the tetrahedron (see the picture).

\sqrt{6} cm

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

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

3 \sqrt{2} cm

1103101208

Level:

Let

A B C D

be a regular tetrahedron with an edge length of

5 cm

. Let

φ

be the angle between the face

A B D

and the base plane

A B C

(see the picture). Choose the correct expression for

φ

\cos φ = \frac{1}{3}

tg φ = 6 \sqrt{3}

tg φ = 3 \sqrt{2}

\cos φ = \frac{2}{3}

1103101207

Level:

Let

A B C D

be a regular tetrahedron with an edge length of

5 cm

. Let

φ

be the angle between the edge

A D

and the base plane

A B C

(see the picture). Choose the correct expression for

φ

\cos φ = \frac{\sqrt{3}}{3}

tg φ = \sqrt{3}

tg φ = \frac{\sqrt{3}}{3}

\cos φ = \sqrt{3}

1103101206

Level:

Let

A B C D E F V

be a regular hexagonal pyramid with a base edge length of

4 cm

and a height of

10 cm

. Find the distance between the line

A C

and the line

F D

(see the picture).

4 cm

2 \sqrt{3} cm

2 \sqrt{2} cm

4 \sqrt{3} cm

1103101205

Level:

Let

A B C D E F V

be a regular hexagonal pyramid with an edge

A B

, where

| A B | = 4 cm

, and an edge

A V

, where

| A V | = 8 cm

. Find the angle between the line

A V

and the base plane

A B C

(see the picture).

60^{\circ}

45^{\circ}

72^{\circ}

30^{\circ}

1103101204

Level:

Let

A B C D E F V

be a regular hexagonal pyramid with a base edge length of

4 cm

and a height of

6 cm

. Let

φ

be the angle between the plane

A F V

and the base plane

A B C

(see the picture). Choose the correct expression for

φ

tg φ = \sqrt{3}

\sin φ = \sqrt{3}

tg φ = \frac{\sqrt{3}}{3}

tg φ = \frac{3}{2}

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