Rhomboid

The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?

Result

|AC| =  6.65 cm

Solution:

sinγsin60=56 γ=arcsin.72168 γ=46.194 β=1806046.194=73.806 AC6sin73.806sin60 AC=61.1088853 AC=6.6533121 cm6.65  cm  \dfrac{ \sin \gamma }{ \sin 60 } = \dfrac{ 5 }{ 6 } \ \\ \gamma = \arcsin .72168 \ \\ \gamma = 46.194^\circ \ \\ \beta = 180-60-46.194 = 73.806^\circ \ \\ \dfrac{ |AC| }{ 6 } \dfrac{ \sin 73.806^\circ }{ \sin 60 } \ \\ |AC| = 6 \cdot 1.1088853 \ \\ |AC| = 6.6533121 \ cm \doteq 6.65 \ \text { cm } \ \\

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