Question

A rhombus of side 20cm has two angles of 60 each .Find the length of diafinals

Answer 1

hello,
for this question we will use trignometry
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
hope this helps,if  like it please mark it as brainliest

Answer 2

Question :

A rhombus of side 20cm has two angles of 60 each .Find the length of diagonals.

Answer :

The length of diagonals are 20 cm and 20√3cm.

Given :

Side of rhombus = 20cm

Angles = 60° each

To find :

The length of diagonals

Solution :

In ΔAOD,

Sin 30° = AO/AD

=> 1/2 = AO/20

=> AO = 20 × 1/2

=> AO = 10cm

∴ Diagonal AC = 2AO =20cm

Now,

Cos 30° = OD/AD

=> √3/2 = OD/20

=> OD = 20 × √3/2

=> OD = 10√3cm

∴Diagonal BD = 2 OD = 2 × 10√3cm

= 20√3cm

Hence, the length of diagonals are 20 cm and 20√3cm.

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