Question

a rhombus has sides of 20 cm and two angles of 60 degree .find the length of the diagonals.

Answer 1

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

Answer 2

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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