Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.

Correct result:

b =  4.641 cm

Solution:

a=10 cm h=a2−(a/2)2=102−(10/2)2=5 3 cm≐8.6603 cm  tan⁡(60∘)=b/x a=2x+b  tan⁡(60∘)⋅ (a−b)/2=b  a/2⋅ tan⁡(60∘)=b(1+tan⁡(60∘)/2)   b=a2⋅ tan⁡60∘1+tan⁡60∘/2=tan⁡π/3=4.641=9719π/6579=4.641 cm

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