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Length of the sides of equilateral triangle

awargi

Hi
can someone please tell me how to do this question:

ive managed to work out part a, and ive written the answers on the question

(edited 12 years ago)

Reply 1

Slumpy

You can do this all with pythagoras' theorem, and using the fact that the triangle is equilateral(for instance, noting |OC'|=|OA'|, and 2*|BA'|=|BC|)

Reply 2

porkstein

The best way to approach questions like this is to just label whatever you can and see where it takes you. So you know each side has length 1, and so you can deduce, for instance, that the distance from C to A' is 1/2. Of course, this isn't particularly helpful, and in fact there's very little you can say about any of the lengths to begin with. But you can start thinking about angles. By symmetry you can deduce that all of the angles in the corners are 30 degrees, and thus (by the fact that angles in a triangle add up to 180 degrees) that all of the angles in the centre are 60 degrees. You could then use some basic trigonometry - SOHCAHTOA - to calculate the lengths. As a starting point, consider the triangle CA'O. You know that this triangle is right-angled, and you know the other two angles and one of the lengths also. That's enough information to begin some calculations.