ABCD is a rhombus whose on angle is 60. find the ratio of its diagonal?
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hi..
In a parallelogram,as you know, diagonals bisect each other . if AC and BD are daigonals and they bisect at point E we get 4 triangles AED , DEC ,CED and AEB.
in triangle AED angle A = 30, D=60 and E=90. since it is a 30-60-90 triangle, if AE (The longer leg) = x then shorter leg is
x/square root(3) and hypotenuse is 2x/square root(3).
so AE = x
=> AC = 2x
DE = x/square root(3)
=> DB = 2x/square root(3)
so BD : AC = 1 : square root(3)
Hope I am right
In a parallelogram,as you know, diagonals bisect each other . if AC and BD are daigonals and they bisect at point E we get 4 triangles AED , DEC ,CED and AEB.
in triangle AED angle A = 30, D=60 and E=90. since it is a 30-60-90 triangle, if AE (The longer leg) = x then shorter leg is
x/square root(3) and hypotenuse is 2x/square root(3).
so AE = x
=> AC = 2x
DE = x/square root(3)
=> DB = 2x/square root(3)
so BD : AC = 1 : square root(3)
Hope I am right
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