Question

ABCD is a rhombus whose diagonal AC makes an angle Alpha with a b if cos alpha is equal to 2 upon 3 and OB is equal to 3 cm find the length of 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