Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body 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 tan25/8 9=tan5π/36=0=45.12 cm
b=86 tan25/8 3=tan5π/36=0=15.04 cm
tan25=cAC c=ACtan25=40.1 cm a=98c=45.12 b=38c=15.04 cm
V=abc=27208 cm3
S=2(ab+bc+ac)=6182 cm2



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