Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees).

Final Answer:

α =  45 °

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ b=8\text{cm} \\ c=10\text{cm} \\ {u}_1=\sqrt{a^2+b^2}=\sqrt{6^2+8^2}=10\text{cm} \\ \tan \alpha =c:u_1=c/u_1 \\ A=\arctan (c/u_1)=\arctan (10/10)\doteq 0.7854\text{rad} \\ \alpha =A\to \text{°}=A\cdot \frac{180}{\pi }\text{°}=0.7854\cdot \frac{180}{\pi }\text{°}=45\text{°}=45^{\circ } \end{gathered}$$

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