a rhombus has sides of 20 cm and two angles of 60 degree .find the length of the diagonals.
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a rhombus has sides of 20 cm and two angles of 60 degree .find the length of the diagonals.
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Answer:
The rhombus has two angles of 60° and other two angles of 120° each.
Let bigger diagonal A=2x and
Smaller diagonal B=2y, then we have:
(sin 30°) / y = (sin 60°)/x = (sin90°)/20
<=> 1/2y = √3/2x = 1/20
=> y =10 cm , x = 10 √3 cm ≈ 17.3 cm
Therefore:
The bigger diagonal of the rhombus is A=2x≈34.6 cm
The smaller diagonal of the rhombus is B=2y=20 cm
inΔAOD
sin30°=AO/AD
1/2=AO/20
AO=10cm
∴diagonal AC=2AO=20cm
now
cos30°=OD/AD
√3/2=OD/20
OD=10√3cm
∴diagonal BD=2OD=20√3cm
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