Question

Find the lengths of diagonals AC and BD. Given AB = 60 cm and ∠ BAD = 60°.

Answer 1

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.