# 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:

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

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#### Following knowledge from mathematics are needed to solve this word math problem:

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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