Diagonals

Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°.

Correct answer:

u₁ =  6.43
u₂ =  7.66

Step-by-step explanation:

$$\begin{gathered} u_1^2=a^2+a^2-2aa\cos 80^{\circ } \\ {u}_1^2=2a^2-2a^2\cos 80^{\circ } \\ {u}_1=a\sqrt{2(1-\cos 80^{\circ })}=6.43 \end{gathered}$$

$$\begin{gathered} \beta =180^{\circ }-80^{\circ }=100^{\circ } \\ {u}_2^2=a^2+a^2-2aa\cos 100^{\circ } \\ {u}_2^2=2a^2-2a^2\cos 100^{\circ } \\ {u}_2=a\sqrt{2(1-\cos 100^{\circ })}=7.66 \end{gathered}$$

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