Diagonals in diamond

In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.

Correct answer:

u1 =  160 cm
u2 =  277.13 cm

Step-by-step explanation:

a=160 cm α=60   u12 = a2+a22aa cos α u12 = 2a22a2 cos α u1=a 2 (1cosα)=a 2 (1cos60° )=160 2 (1cos60° )=160 2 (10.5)=160=160 cm
β=180α=18060=120  u22 = a2+a22aa cos β u22 = 2a22a2 cos β u2=a 2 (1cosβ)=a 2 (1cos120° )=160 2 (1cos120° )=160 2 (1(0.5))=277.13=277.13 cm



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