Pyramid

Pyramid has a base a = 3cm and height in v = 15 cm.

a) calculate angle between plane ABV and base plane
b) calculate angle between opposite side edges.

Correct answer:

α =  84.29 °
β =  11.36 °

Step-by-step explanation:

$$\begin{gathered} a=3cm \\ v=15cm \\ \tan \alpha ={\displaystyle \frac{v}{a\mathrm{/}2}}={\displaystyle \frac{15}{3\mathrm{/}2}} \\ \alpha =\arctan {\displaystyle \frac{15}{3\mathrm{/}2}}=84.29\text{°}=84\mathrm{°}17^{\mathrm{\prime }}22\mathrm{"} \end{gathered}$$

$$\begin{gathered} \tan \beta \mathrm{/}2={\displaystyle \frac{a}{\sqrt{v^2+(a\mathrm{/}2{)}^2}}} \\ \beta =2\arctan {\displaystyle \frac{a}{\sqrt{v^2+(a\mathrm{/}2{)}^2}}} \\ \beta =2\arctan 0.0995 \\ \beta =11.36\text{°}=11\mathrm{°}21^{\mathrm{\prime }}54\mathrm{"} \end{gathered}$$

Try another example

Related math problems and questions:

• Quadrilateral pyramid
  The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
• Tetrahedral pyramid
  Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm², and the deviation angle of the side edges from the plane of the base is 60 degrees.
• Side edges
  The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
• Cone
  The rotating cone volume is 9.42 cm³, with a height 10 cm. What angle is between the side of the cone and its base?
• Pentagonal pyramid
  Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
• 4side pyramid
  Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
• Regular quadrangular pyramid
  The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
• Pyramid 8
  Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
• Angle of two lines
  There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
• Pyramid - angle
  Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees.
• Hexagonal pyramid
  Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
• 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.
• Perimeter of triangle
  In the triangle, ABC angle A is 60° angle B is 90°, and side size c is 15 cm. Calculate the triangle circumference.
• Square pyramid
  Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.
• Octagonal pyramid
  Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
• Cone side
  Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
• Truncated pyramid
  Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm and the angle that the side wall with the base is 42 degrees