Tetrahedral pyramid 8

Let all the side edges of the tetrahedral pyramid ABCDV be equally long and its base let us be a rectangle. Find its volume if you know the deviations A=52° B=56° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h=100.

Final Answer:

V =  702645.08

Step-by-step explanation:

$$\begin{gathered} \alpha =52{}^{\circ } \\ \beta =56{}^{\circ } \\ h=100 \\ \tan \alpha =\frac{h}{b/2} \\ \tan \beta =\frac{h}{a/2} \\ b=\frac{2\cdot h}{\tan (\alpha )}=\frac{2\cdot 100}{\tan (52°)}\doteq 156.2571 \\ a=\frac{2\cdot h}{\tan (\beta )}=\frac{2\cdot 100}{\tan (56°)}\doteq 134.9017 \\ S=a\cdot b=134.9017\cdot 156.2571\doteq 21079.3524 \\ V=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot 21079.3524\cdot 100=702645.08\doteq 7.0\cdot 10^5 \end{gathered}$$

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