Hi Amy,

What I remember is that for a 30-60-90 triangle the sides are in the ratio of

1:2:sqrt(3)

2 is the largest of the three numbers so it is the length of the hypotenuse, and 1 is the smallest of the three numbers so it is the length of the side opposite the 30^o angle.

In your triangle the length of the side opposite the 60^o angle is 6 inches. In my triangle the length of that side is sqrt(3) inches. Thus the sides in your triangle are 6/sqrt(3) times as large as the sides in my triangle. Hence your triangle has side lengths

1  ⁶/_sqrt(3) =  ⁶/_sqrt(3)

2  ⁶/_sqrt(3) = ¹²/_sqrt(3) and

sqrt(3)  ⁶/_sqrt(3) = 6

Penny

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