Diagonals of a prism

The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.

Correct answer:

A =  63.4349 °

Step-by-step explanation:

$$\begin{gathered} a=3\text{ dm } \\ b=4\text{ dm } \\ c=1\text{ m}\to \text{ dm}=1\cdot 10\text{ dm}=10\text{ dm } \\ {d}_1=\sqrt{a^2+b^2}=\sqrt{3^2+4^2}=5\text{ dm } \\ \tan A=c\mathrm{/}{d}_1 \\ \alpha =\arctan (c\mathrm{/}{d}_1)=\arctan (10\mathrm{/}5)\doteq 1.1071\text{ rad } \\ A=\alpha {\to }^{\circ }=\alpha \cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=1.1071\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=63.435^{\circ }=63.4349^{\circ }=63^{\circ }26^{\mathrm{\prime }}6\mathrm{"} \end{gathered}$$

Try another example

Related math problems and questions:

• Diagonal
  Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
• Space diagonal angles
  Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
• Angle of diagonal
  The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
• Wall and body diagonals
  Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.
• Body diagonal
  Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
• Wall and body diagonals
  The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
• Height of the cuboid
  Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
• Cube - angles
  Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
• Prism
  Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
• Quadrilateral prism
  The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
• Box
  Calculate the angle between box base 9 x 14 and body diagonal length 18.
• Prism diagonal
  The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
• Triangular prism
  Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)
• Concrete block
  Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
• Cuboid
  Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
• Prism - box
  The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.