ABCD is a rhombus angle D= 60° .find AC=BD
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Rhombus ABCD, => diagonals AC & BD bisect at right angles. Point of intersection is O.
& also diagonals bisect interior angles of it. So, if in right triangle AOB
tan 30° = OB/OA = 1/√3
=> OB = x & OA = √3x
=> DB = 2x
& AC = 2√3x
=> DB/AC = 2x/2√3x
=> DB/AC = 1/√3
=> Ratio of diagonal opposite to smaller 60° angle to that of diagonal opposite to greater 120° angle = 1 : √3
I Hope It Will Help!
^_^
Rhombus ABCD, => diagonals AC & BD bisect at right angles. Point of intersection is O.
& also diagonals bisect interior angles of it. So, if in right triangle AOB
tan 30° = OB/OA = 1/√3
=> OB = x & OA = √3x
=> DB = 2x
& AC = 2√3x
=> DB/AC = 2x/2√3x
=> DB/AC = 1/√3
=> Ratio of diagonal opposite to smaller 60° angle to that of diagonal opposite to greater 120° angle = 1 : √3
I Hope It Will Help!
^_^
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