Diagonals in diamond

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

Correct answer:

u₁ =  160
u₂ =  277.13

Step-by-step explanation:

$$\begin{gathered} u_1^2=a^2+a^2-2aa\cos 60^{\circ } \\ {u}_1^2=2a^2-2a^2\cos 60^{\circ } \\ {u}_1=a\sqrt{2(1-\cos 60^{\circ })}=160 \end{gathered}$$

$$\begin{gathered} \beta =180^{\circ }-60^{\circ }=120^{\circ } \\ {u}_2^2=a^2+a^2-2aa\cos 120^{\circ } \\ {u}_2^2=2a^2-2a^2\cos 120^{\circ } \\ {u}_2=a\sqrt{2(1-\cos 120^{\circ })}=277.13 \end{gathered}$$

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