Two of the angles of a rhombus are of 60 each. find the length of the diagonals if each side of the rhombus is 10 cm
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Two angles are 60°, that means the smallest diagonal divides it into two equal equilateral triangle.
And the diagonal bisects each other at 90°.
Being an equilateral triangle, length of smallest diagonal is 10 cm
Length of another diagonal,
(L/2)² = (10²) - (5)²
⇒L²/4 = 100 - 25
= 75
⇒L² = 75×4
⇒L = 10√3 cm
So, the length of diagonal will be 10 cm and 10√3 cm
And the diagonal bisects each other at 90°.
Being an equilateral triangle, length of smallest diagonal is 10 cm
Length of another diagonal,
(L/2)² = (10²) - (5)²
⇒L²/4 = 100 - 25
= 75
⇒L² = 75×4
⇒L = 10√3 cm
So, the length of diagonal will be 10 cm and 10√3 cm
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