Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.

Correct answer:

a =  39.3867 dm
b =  23.2337 dm
c =  26.7934 dm

Step-by-step explanation:

$$\begin{gathered} u=53\text{ dm } \\ A=42^{\circ } \\ B=64^{\circ } \\ a=u\cdot \cos A^{\circ }=u\cdot \cos 42^{\circ }=53\cdot \cos 42^{\circ }=53\cdot 0.743145=39.387=39.3867\text{ dm} \end{gathered}$$

$b=u\cdot \cos B^{\circ }=u\cdot \cos 64^{\circ }=53\cdot \cos 64^{\circ }=53\cdot 0.438371=23.234=23.2337\text{ dm}$

$$\begin{gathered} u_2=\sqrt{a^2+b^2}=\sqrt{39.3867^2+23.2337^2}\doteq 45.7287\text{ dm } \\ c=\sqrt{u^2-u_2^2}=\sqrt{53^2-45.7287^2}=26.7934\text{ dm} \end{gathered}$$

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