If the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the lengths of the diagonals of the rhombus.
Answer :
Each side of a rhombus = 8 cm
One angle = 60°
∠OAB = 60°/2 = 30°
In right ∠AOB
sin 30° = OB/AB
½ = OB/8
OB = 8/2 = 4 cm
BD = 2OB = 2 × 4 = 8 cm
cos 30° = AO/AB
√3/2 = AO/8
AO = 8√3/2 = 4√3
AC = 4√3 × 2 = 8 √3 cm
Hence,
The length of the diagonals of the rhombus are 8 cm and 8√3 cm.
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