Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, c has dimensions in the ratio of 9:3:8. If you know that the diagonal wall AC is 86 cm, and the angle between AC and space diagonal AG is 25 degrees.

Correct result:

a =  45.12 cm
b =  15.04 cm
c =  40.1 cm
V =  27208 cm³
S =  6182 cm²

Solution:

$a=86\cdot \tan 25^{\circ }\mathrm{/}8\cdot 9=\tan 5\pi \mathrm{/}36=0=45.12\text{ cm}$

$b=86\cdot \tan 25^{\circ }\mathrm{/}8\cdot 3=\tan 5\pi \mathrm{/}36=0=15.04\text{ cm}$

$$\begin{gathered} \tan 25^{\circ }={\displaystyle \frac{c}{\mathrm{\mid }AC\mathrm{\mid }}} \\ c=\mathrm{\mid }AC\mathrm{\mid }\tan 25^{\circ }=40.1\text{ cm } \\ a={\displaystyle \frac{9}{8}}c=45.12 \\ b={\displaystyle \frac{3}{8}}c=15.04\text{ cm} \end{gathered}$$

$V=abc=27208{\text{cm}}^3$

$S=2(ab+bc+ac)=6182{\text{cm}}^2$

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