Question 42

One of the four angles of a rhombus is $$60°$$. If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is


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=8 cm, angle DAB =60°.
Consider the triangle AOB,
$$\angle OAB$$=30° (diagonal of a rhombus bisects the angle)
$$\angle AOB$$=90°(diagonals of a rhombus bisect each other at right angles)
So triangle AOB is right angled at O. Hence ,
Cos 30°= OA/AB
OA=8*(√3/2) cm.
Since, longer diagonal AC= $$2\times OA$$
therefore, AC=8√3 cm

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