Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.

Correct result:

a =  39.3867 dm
b =  23.2337 dm
c =  26.7934 dm

Solution:

u=53 dm A=42∘ B=64∘  a=u⋅ cos⁡A∘=u⋅ cos⁡42∘ =53⋅ cos⁡42∘ =53⋅ 0.743145=39.387=39.3867 dm
b=u⋅ cos⁡B∘=u⋅ cos⁡64∘ =53⋅ cos⁡64∘ =53⋅ 0.438371=23.234=23.2337 dm
u2=a2+b2=39.38672+23.23372≐45.7287 dm c=u2−u22=532−45.72872=26.7934 dm

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