Question

ABCD is a rhombus whose diagonal AC makes an angle a with side CD where cos a = 2/3. If PD = 4 cm, then find the side and the diagonals of the rhombus.​

Answer 1

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

Step-by-step explanation:

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