question_answer

The lengths of diagonals of a rhombus bear the ratio \[1:\sqrt{3}\]. The angles of the rhombus are

A) \[30{}^\circ ,\text{ }60{}^\circ \]

B) \[30{}^\circ ,\text{ }120{}^\circ \]

C) \[60{}^\circ ,\text{ }120{}^\circ \]  

D) \[90{}^\circ ,\text{ }120{}^\circ \]

Correct Answer: C

Solution :

 Since the diagonals of a rhombus bisect each other at right angles, therefore \[\frac{OC}{OD}=\frac{AC}{BD}=\sqrt{3}\]                 or            \[\tan \angle ODC=\sqrt{3}\] Consequently, \[\angle ODC={{60}^{o}}\]                                 \[\angle ADC={{120}^{o}}\] Also                       \[\angle OCD={{30}^{o}}\] Therefore           \[\angle BCD={{60}^{o}}\] Hence the angle of the rhombus are \[{{60}^{o}},{{120}^{o}}.\]