Diagonals of a prism

The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal.

Final Answer:

A =  63.4349 °

Step-by-step explanation:

$$\begin{gathered} a=3\text{dm} \\ b=4\text{dm} \\ c=1\text{m}\to \text{dm}=1\cdot 10\text{dm}=10\text{dm} \\ {d}_1=\sqrt{a^2+b^2}=\sqrt{3^2+4^2}=5\text{dm} \\ \tan A=c/d_1 \\ \alpha =\arctan (c/d_1)=\arctan (10/5)\doteq 1.1071\text{rad} \\ A=\alpha \to \text{°}=\alpha \cdot \frac{180}{\pi }\text{°}=1.1071\cdot \frac{180}{\pi }\text{°}=63.435\text{°}=63.4349^{\circ }=63°26^{\prime }6" \end{gathered}$$

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