Question

if one angle of a rhombus is 60 then find the ratio of the length of its diagonals.

Answer 1

One angle of rhombus is given to be 60 degrees and its side is given 10 cm. Then, what will be the length of longer diagonal?

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8 ANSWERS



Rahul Singh Yadav, Trigonometry is fun...

Answered Feb 20, 2016

Consider a rhombus ABCD,
and let the diagonals bisect each other at point O.

So, assuming AC to be the longer diagonal,

We are given,
AB=10 cm, angle DAB =60°.

Consider the triangle AOB,

angle OAB=30° (diagonal of a rhombus bisects the angle)

Also, 

angle AOB=90°(diagonals of a rhombus bisect each other at right angles)

So triangle AOB is right angled at O. 

Using, trigonometry
           Cos 30°= OA/AB
or                OA=AB*(√3/2)
or                 OA=10*(√3/2) cm.

Answer 2

yes i think the above answer is correct