Rhombus

Internal angles of rhombus is in ratio 2:3.

How many times is the shorter diagonal longer than side of rhombus?

Correct result:

x =  1.18

Solution:

α:β=α2:β2=2:3 α2=22+3⋅90∘=36∘ x=2sin⁡(α2)=1.18\alpha : \beta = \dfrac{ \alpha}{2} : \dfrac{ \beta}{2} = 2:3 \ \\ \dfrac{ \alpha}{2} = \dfrac{ 2 }{ 2+3} \cdot 90 ^\circ = 36 ^\circ \ \\ x = 2 \sin(\dfrac{ \alpha}{2}) = 1.18

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