Metric properties

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}

Level:

Consider a cone of base radius

r

and a special shape: the shape is such that the volume of the cone is related to the base radius by the formula

V = π r^{3}

. Find the angle between the side of the cone and the base. Round your answer to two decimal places.

{71.57}^{\circ}

45^{\circ}

{63.43}^{\circ}

Level:

Let

ω

be the angle between the solid diagonal of a box and the base of this box. Find the expression which allows to find

ω

tg ω = \frac{\sqrt{2}}{2}

\cos ω = \frac{\sqrt{2}}{2}

\sin ω = \frac{\sqrt{2}}{2}

cotg ω = \frac{\sqrt{2}}{2}

Level:

Find the angle between the side of a cube and the cube’s space diagonal. Round the result to two decimal places.

{35.26}^{\circ}

45^{\circ}

{54.76}^{\circ}

Level:

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

2 cm

. The height of the pyramid is

4 cm

. Find the angle between the lateral side of the pyramid and the base. Round your result to two decimal places.

{75.96}^{\circ}

{70.52}^{\circ}

{79.98}^{\circ}