Rhombus

One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.

Result

u =  19.801 cm
a =  10.678 cm

Solution:

v=8 B=136 tanB/2=u/v u=v tan(B/2)=8 tan(136/2)19.8007=19.801  cm v = 8 \ \\ B = 136 \ \\ \tan B/2 = u/v \ \\ u = v \cdot \ \tan(B/2) = 8 \cdot \ \tan(136/2) \doteq 19.8007 = 19.801 \ \text{ cm }
a=(u/2)2+(v/2)2=(19.8007/2)2+(8/2)210.678=10.678  cm a = \sqrt{ (u/2)^2+(v/2)^2 } = \sqrt{ (19.8007/2)^2+(8/2)^2 } \doteq 10.678 = 10.678 \ \text{ cm }

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