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 answer:

e =  4.4721 cm
f =  8.9443 cm

Step-by-step explanation:

a=5 cm S=20 cm2  S=ah h=S/a=20/5=4 cm  h=a sin(A) A=π180°arcsin(h/a)=π180°arcsin(4/5)53.1301   e=a 22 cosA°=a 22 cos53.130102354156° =5 22 cos53.130102354156° =5 22 0.6=4.472=4.4721 cm
f=a 2+2 cosA°=a 2+2 cos53.130102354156° =5 2+2 cos53.130102354156° =5 2+2 0.6=8.944=8.9443 cm

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Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2   video3

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