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=180πarcsin(h/a)=180πarcsin(4/5)53.1301  e=a 22 cosA=a 22 cos53.1301023542 =5 22 cos53.1301023542 =5 22 0.6=4.472=4.4721 cm
f=a 2+2 cosA=a 2+2 cos53.1301023542 =5 2+2 cos53.1301023542 =5 2+2 0.6=8.944=8.9443 cm



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