Pyramid - angles

In a regular pyramid in which the edge of the base is | AB | = 4 cm; height = 6 cm, calculate the angle of the lines AV and CV, V = vertex.

Final Answer:

X =  50.4788 °

Step-by-step explanation:

$$\begin{gathered} a=4\text{cm} \\ h=6\text{cm} \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 4=4\sqrt{2}\text{cm}\doteq 5.6569\text{cm} \\ x=u/2=5.6569/2=2\sqrt{2}\text{cm}\doteq 2.8284\text{cm} \\ {X}_1=\frac{180°}{\pi }\cdot \arctan (x/h)=\frac{180°}{\pi }\cdot \arctan (2.8284/6)\doteq 25.2394{}^{\circ } \\ X=2\cdot X_1=2\cdot 25.2394=50.4788^{\circ }=50°28^{\prime }44" \end{gathered}$$

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