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?

Correct answer:

x =  36.8699 °

Step-by-step explanation:

$$\begin{gathered} h=6\text{ cm } \\ a=4\text{ cm } \\ {s}_1=a\mathrm{/}2=4\mathrm{/}2=2\text{ cm } \\ {s}_2=\sqrt{s_1^2+h^2}=\sqrt{2^2+6^2}=2\sqrt{10}\text{ cm}\doteq 6.3246\text{ cm } \\ \tan x\mathrm{/}2=s_1\mathrm{/}h \\ x=2\cdot {\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arctan (s_1\mathrm{/}h)=2\cdot {\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arctan (2\mathrm{/}6)=36.8699\text{°}=36\mathrm{°}52^{\mathrm{\prime }}12\mathrm{"} \end{gathered}$$

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