Triangle and Square
----David Jaffe (Y9)
You have an equilateral triangle of sides 1cm . What is the area
of the smallest square that can cover it?
60°
1 cm
Corner of square is 90, angle of equilateral triangle is 60. So to ensure the square has, the shortest side, spilt the difference (30) in half on either side of the 60, because this ensures the biggest angle that can be cosined on both sides, and a bigger cosine is a shorter square side. Also the two 1cos15 have to be the same meaning it is a square
15°
15°
75°
75°
45°
45°
Adj/hyp=Cos angle A/1=Cos15 A=0.9659 A squared=0.933
Answer: Area of square is 0.933 cm 2 .
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