. A rhombus of side 14 cm has two angles of 60 degree each. Find the length of the diagonals of the rhombus.
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Given : a rhombus
side 14 cm
two angles of 60° each
To Find : Diagonal LN
Solution:
A rhombus has all 4 sides equal = 14 cm
two angles of 60 degrees each
Cosine law : a² + b² - c² = 2abcosC
=> 14² + 14² -x² = 2(14)(14)Cos60°
=> 14² + 14² - x² = 14²
=> x² = 14²
=> x = 14
other two angles of 180 - 60 = 120 degrees each
=> 14² + 14² -y² = 2(14)(14)Cos120°
=> 14² + 14² - y² = -14²
=> y² =3* 14²
=> y = 14√3
Diagonal length are 14 and 14√3
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