an acute angle made by a side of a parallelogram with other pair of parallel sides is 30 degree if the distance between these parallel side is 10cm then the other side is?
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Answer:
GivenABCDisaparallelogram.
AB∥DCandAD∥BC.
∠DAB=60°,
distancebetweentwoparallelsidesABandDC(h)=6
3
cm
In \: \triangle ADM, \angle {AMD} = 90\degreeIn△ADM,∠AMD=90°
Sin 60\degree = \frac{MD}{AD}Sin60°=
AD
MD
\implies \frac{\sqrt{3}}{2} = \frac{6\sqrt{3}}{AD}⟹
2
3
=
AD
6
3
\implies AD = 6\sqrt{3}\times \frac{2}{\sqrt{3}}⟹AD=6
3
×
3
2
\implies AD = 6 \times 2 = 12 \:cm⟹AD=6×2=12cm
Therefore.,
\red{ Required \: length \:of \:the \:side }\green {= 12 \:cm }Requiredlengthoftheside=12cm
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