If AC = 8 cm and BD = 6 cm, find sin ∠OCD.

The diagonals AC and BD of a rhombus ABCD meet at O. If AC = 8 cm and BD = 6 cm, find sin ∠OCD.

Answer :

Diagonals AC and BD of rhombus ABCD meet at O

AC = 8 cm and BD = 6 cm

O is the mid point of AC

AO = OC = AC/2 = 8/2 = 4 cm

O is the mid point of BD

BO = OD = BD/2 = 6/2 = 3 cm

In right angled ∆COD

CD² = OC² + OD²

CD² = 4² + 3²

CD² = 16 + 9 = 25

⇒ CD² = 5²

⇒ CD = 5 cm

In right angled ∆COD

sin ∠OCD = perpendicular/ hypotenuse

sin ∠OCD = OD/CD = 3/5

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