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.

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

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