Cuboid

Find the dimensions a, b, and c of a cuboid whose space diagonal is d = 6 dm and makes an angle α = 35° with edge a and an angle β = 66° with edge b.

Final Answer:

a =  4.91 dm
b =  1.4 dm
c =  3.14 dm

Step-by-step explanation:

$$\begin{gathered} u=6 \\ \alpha =35{}^{\circ } \\ \beta =66{}^{\circ } \\ a=u\cdot \cos \alpha =u\cdot \cos 35°=6\cdot \cos 35°=6\cdot 0.819152=4.91=4.91\text{dm} \end{gathered}$$

$b=u\cdot \sin \alpha \cdot \cos \beta =u\cdot \sin 35°\cdot \cos 66°=6\cdot \sin 35°\cdot \cos 66°=6\cdot 0.573576\cdot 0.406737=1.4=1.4\text{dm}$

$c=u\cdot \sin \alpha \cdot \sin \beta =u\cdot \sin 35°\cdot \sin 66°=6\cdot \sin 35°\cdot \sin 66°=6\cdot 0.573576\cdot 0.913545=3.14=3.14\text{dm}$

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