Question

a rhombus of side 10cm has two angles of 60° each. find the length of the diagonals.​

Answer 1

Answer:

Length of diagonal =10 cm (BD) and AC=10√3 cm

Step-by-step explanation:

We can assume that ABCD is Rhombus with center O whose side is 10 cm and

Two angle=60°(∠BAD=∠BCD)

Diagonals of a parallelogram are bisect each other.(AO=OC,BO=OD)

Sin 30°=OB/AB

1/2=OB/10⇒OB=5 cm ∴BD=2(OB)⇒BD=2(5)=10 cm

∴BD=10 cm

cos 30°=OA/AB

√3/2=OA/10⇒OA=5√3 cm ∴AC=2(OC)=10√3cm

  ∴AC=10√3 cm.

∴ the length of the diagram is BD=10 cm and AC=10√3 cm.