Diagonals of the rhombus

How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?

Correct result:

e =  4.4721 cm
f =  8.9443 cm

Solution:

a=5 cm S=20 cm2  S=ah h=S/a=20/5=4 cm  h=a⋅ sin⁡(A) A=180∘π⋅arcsin⁡(h/a)=180∘π⋅arcsin⁡(4/5)≐53.1301∘  e=a⋅ 2−2⋅ cos⁡A∘=a⋅ 2−2⋅ cos⁡53.130102354156∘ =5⋅ 2−2⋅ cos⁡53.130102354156∘ =5⋅ 2−2⋅ 0.6=4.472=4.4721 cm
f=a⋅ 2+2⋅ cos⁡A∘=a⋅ 2+2⋅ cos⁡53.130102354156∘ =5⋅ 2+2⋅ cos⁡53.130102354156∘ =5⋅ 2+2⋅ 0.6=8.944=8.9443 cm

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