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=40° B=70° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h=16.

Correct answer:

V =  2368.9234

Step-by-step explanation:

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

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