Question

ABCD is a rhombus whose diagonal AC makes an angle alpha with AB. If cos alpha =2/3 and OB =3cm , find the diagonals AC and BD?​

Answer 1

Let the diagonals AC and BD intersect each other at O

Thus according to question

Angle BAO = Angle alpha

and

Cos Alpha = 2/3

Thus in triangle AOB

Cos alpha = AO / AB

and Sin alpha = OB/AB

1/3 = 3/AB

Thus   AB = 9

SO tan alpha = OB/AO

1/2 = 3/AO

AO = 6

Thus      AC= 12

and        BD = 6

Answer 2

$\bf\large\underline\blue{Answer:-}$

Let the diagonals AC and BD intersect each other at O

Thus according to question

Angle BAO = Angle alpha

and

Cos Alpha = 2/3

Thus in triangle AOB

Cos alpha = AO / AB

and Sin alpha = OB/AB

1/3 = 3/AB

Thus AB = 9

SO tan alpha = OB/AO

1/2 = 3/AO

AO = 6

Thus AC= 12

and BD = 6