Mathematics

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

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Since, diagonals of rhombus bisect each other.

∴ O is the mid point of AC.

In right angled ∆COD,

⇒ CD² = OC² + OD² [By pythagoras theorem]

⇒ CD² = 4² + 3²

⇒ CD² = 16 + 9

⇒ CD² = 25

⇒ CD = $\sqrt{25}$

⇒ CD = 5 cm.

sin ∠OCD = $\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}$

sin ∠OCD = $\dfrac{OD}{CD} = \dfrac{3}{5}$ .

Hence, sin ∠OCD = $\dfrac{3}{5}$ .

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