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Question
Find the lengths of diagonals AC and BD. Given AB = 60 cm and ∠ BAD = 60°.
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Solution
We know, diagonals of a rhombus bisect each other at right angles and also bisect the angle of the vertex.
The figure is shown below:
Now
OA = OC =`(1)/(2)`AC, OB = OD =`(1)/(2)`BD; ∠AOB = 90°
And ∠OAB = `(60°)/(2)` = 30°
Also given AB = 60 cm
In right triangle AOB
sin 30° = `"OB"/"AB"`
`(1)/(2) = "OB"/(60)`
OB = 30 cm
Also
cos 30° = `"OA"/"AB"`
`sqrt(3)/(2) = "OA"/60`
OA = 51.96 cm
Therefore,
Length of diagonal AC = 2 x OA = 2 x 51.96 = 103.92 cm.
Length of diagonal BD = 2 x OB = 2 x 30 = 60 cm.
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