Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the pyramid.

Correct result:

V =  2368.9234

Solution:

$$\begin{gathered} A=40^{\circ } \\ B=70^{\circ } \\ h=16 \\ \tan A={\displaystyle \frac{h}{b\mathrm{/}2}} \\ \tan B={\displaystyle \frac{h}{a\mathrm{/}2}} \\ b=2\cdot h\mathrm{/}\tan (A)=2\cdot 16\mathrm{/}\tan (40^{\circ })\doteq 38.1361 \\ a=2\cdot h\mathrm{/}\tan (B)=2\cdot 16\mathrm{/}\tan (70^{\circ })\doteq 11.647 \\ S=a\cdot b=11.647\cdot 38.1361\doteq 444.1731 \\ V={\displaystyle \frac{1}{3}}\cdot S\cdot h={\displaystyle \frac{1}{3}}\cdot 444.1731\cdot 16=2368.9234 \end{gathered}$$

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