Question

The length of each side of a rhombus is 8cm. and its one angle is
60⁰.Find the length of the diagonals of the rhombus.​

Answer 1

In triangle AOB,

<OAB=30°(Diagonals of rhombus bisect the angles)

<A+<B=180°(Co int. <s)

60+<B=180°

<B=120°

<OBA=120/2 i.e.60°(Same statement)

A.T.Q-

sin 30°=OB/8

°•° sin 30°=1/2

•°•1/2=OB/8

By cross multiplication

OB=4 cm

•°•BD=4+4 i.e.8 cm

Now,

sin 60°=OA/8

rt3/2=OA/8

By cross multiplication

OA=4rt3

•°•AC=4rt3+4rt3 i.e.8rt3

LENGTH OF DIAGONALS IS-

8 CM , 8RT3 CM

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