Regular quadrangular pyramid

The height of the regular quadrilateral pyramid is 6 cm, and the length of the base is 4 cm. What is the angle between the ABV and BCV planes? ABCD is the base, V is the vertex.

Final Answer:

α =  36.8699 °

Step-by-step explanation:

$$\begin{gathered} h=6\text{cm} \\ a=4\text{cm} \\ {s}_1=a/2=4/2=2\text{cm} \\ {s}_2=\sqrt{s_1^2+h^2}=\sqrt{2^2+6^2}=2\sqrt{10}\text{cm}\doteq 6.3246\text{cm} \\ \tan \alpha /2=s_1/h \\ {\alpha }_1=2\cdot \arctan (s_1/h)=2\cdot \arctan (2/6)\doteq 0.6435\text{rad} \\ \alpha ={\alpha }_1\to \text{°}={\alpha }_1\cdot \frac{180}{\pi }\text{°}=0.6435\cdot \frac{180}{\pi }\text{°}=36.87\text{°}=36.8699^{\circ }=36°52^{\prime }12" \end{gathered}$$

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