Question

ABCD is a rhombus whose diagonal AC is 10cm long and it makes an angle theta with the side AB of the rhombus such that tan theta = 3/5. find the length of side of the rhombus. ​

Answer 1

ABCD is a rhombus whose diagonal AC is 10cm long and it makes an angle theta with the side AB of the rhombus such that tan theta = 3/5. find the length of side of the rhombus.

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

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