Prove that the distance between two opposite edges of a regular hexagon of side length root 3 is a rational value.

Can someone please explain why they have used pythagoras and what led them to use it? I don't understand the mark scheme. I assumed maybe sine/ cosine rule would be involved as 120 degrees is the angle in a regular hexagon.

Can someone please explain why they have used pythagoras and what led them to use it? I don't understand the mark scheme. I assumed maybe sine/ cosine rule would be involved as 120 degrees is the angle in a regular hexagon.

(edited 4 years ago)

Original post by Sidd1

Prove that the distance between two opposite edges of a regular hexagon of side length root 3 is a rational value.

Can someone please explain why they have used pythagoras and what led them to use it? I don't understand the mark scheme. I assumed maybe sine/ cosine rule would be involved as 120 degrees is the angle in a regular hexagon.

Can someone please explain why they have used pythagoras and what led them to use it? I don't understand the mark scheme. I assumed maybe sine/ cosine rule would be involved as 120 degrees is the angle in a regular hexagon.

That answer is wrong. Have you sketched it?

Original post by mqb2766

That answer is wrong. Have you sketched it?

How do you know it's wrong? Yeah I have I'll upload it now

Original post by Sidd1

How do you know it's wrong? Yeah I have I'll upload it now

The hexagon is made from 6 identical equllateral triangles of side length sqrt(3). The center is where the vertices coincide. Can you add this?

if you split the one of the equilateral triangles into two isosceles triangles, you have angles 90 degrees - right angle, 60 degrees - 120 degrees / 2, and 30 degrees - 180-90-60. Since we split each equilateral triangle into two isosceles, the length of one of the sides is root 3 / 2. From there, we can use the sin rule. x / sin60 = root 3 / 2 / sin30. rearrange for x (x = sin60 x root 3 / 2 / sin30) and you get an answer of 3/2.

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