Mark M. answered • 06/10/16
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Mathematics Teacher - NCLB Highly Qualified
The height divides the triangle into two 30-60-90 triangles.
The height is √3 / 2 times the side (hypotenuse), or x√3 /2.
The area of the triangle is (1/2)(x)(x√3/2), or x2√3/4.
Amy S.
I mean x√3/2
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06/10/16
Mark M.
In a 30-60-90 triangle, the side opposite the 30° angle is one-half of the hypotenuse.
The side opposite the 60° is √3/2 of the hypotenuse.
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06/10/16
Amy S.
If you don't mind, could you show me your full working?
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06/10/16
Mark M.
Draw and equilateral triangle. Label each side "x."
Draw an altitude from the base to the opposite vertex. Label it "a."
You now have two triangles each a 30-60-90 triangle.
The side "x" is the hypotenuse. One-half of the base is the short leg.
The altitude is the long leg.
By Pythagoras:
x2 = (x/2)2 + a2
x2 = x2/4 + a2
x2 - x2/4 = a2
3x2/4 = a2
x√3 / 2 = a
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06/10/16
Amy S.
06/10/16