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.

Result

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

Solution:

a=86 tan((25rad)=(25 π180 )=)/8 9=45.12  cm a=86 \cdot \ \tan( (25^\circ \rightarrow rad) = (25 \cdot \ \dfrac{ \pi }{ 180 } \ ) = )/ 8 \cdot \ 9 = 45.12 \ \text { cm }
b=86 tan((25rad)=(25 π180 )=)/8 3=15.04  cm b=86 \cdot \ \tan( (25^\circ \rightarrow rad) = (25 \cdot \ \dfrac{ \pi }{ 180 } \ ) = )/ 8 \cdot \ 3 = 15.04 \ \text { cm }
tan25=cAC c=ACtan25=40.1  cm  a=98c=45.12 b=38c=15.04  cm \tan 25^\circ = \dfrac{c}{|AC|} \ \\ c = |AC| \tan 25^\circ = 40.1 \ \text { cm } \ \\ a = \dfrac{ 9 }{ 8 } c = 45.12 \ \\ b = \dfrac{ 3 }{ 8 } c = 15.04 \ \text { cm }
V=abc=27208 cm3 V = abc = 27208 \ cm^3
S=2(ab+bc+ac)=6182 cm2 S = 2(ab+bc+ac) = 6182 \ cm^2







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See also our right triangle calculator. Tip: Our volume units converter will help you with the conversion of volume units. Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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