Cube - angles

Calculate the angle alpha (α) between the face diagonal and the base of a cube. Calculate the angle beta (β) between the space diagonal and the base of the cube.

Final Answer:

α =  45 °
β =  35.3 °

Step-by-step explanation:

$$\begin{gathered} A=\arctan (\frac{1}{1})\doteq 0.7854\text{rad} \\ \alpha =A\to \text{°}=A\cdot \frac{180}{\pi }\text{°}=0.7854\cdot \frac{180}{\pi }\text{°}=45\text{°}=45^{\circ } \end{gathered}$$

$$\begin{gathered} B=\arctan (\frac{1}{\sqrt{1+1}})\doteq 0.6155\text{rad} \\ \beta =B\to \text{°}=B\cdot \frac{180}{\pi }\text{°}=0.6155\cdot \frac{180}{\pi }\text{°}=35.3\text{°}=35.3^{\circ }=35°15^{\prime }52" \end{gathered}$$

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