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 with the diagonal of the base.

Correct answer:

A =  63.4349 °

Step-by-step explanation:

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

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