Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°

Result

a =  5.16 dm
b =  3.91 dm
c =  6.25 dm

Solution:

a=9⋅cos(55∘)=5.16 dma = 9 \cdot cos(55 ^\circ ) = 5.16 \ \text{dm}
b=9⋅sin(55∘)⋅cos(58∘)=3.91 dmb = 9 \cdot sin(55 ^\circ ) \cdot cos(58 ^\circ ) = 3.91 \ \text{dm}
c=9⋅sin(55∘)⋅sin(58∘)=6.25 dmc = 9 \cdot sin(55 ^\circ ) \cdot sin(58 ^\circ ) = 6.25 \ \text{dm}

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