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# Each triangle is a 30-60-90 triangle

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Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the shorter leg of the smaller triangle?

Nov 4, 2020

#1
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30-60-90 triangles have a property where the shortest side is $$\frac{1}{2}$$ of the longest side. It also has a property where the other leg is $$\frac{\sqrt3}{2}$$ of the longest side in a triangle.

Because the triangles are 30 - 60 - 90 triangles we know that the length of the hypotenuse of the smaller triangle is $$16 \cdot \frac{\sqrt3}{2} = 8\sqrt3$$.

And to find the shortest side of this triangle we refer to what is above showing us that the shorter leg of the smallest triangle is $$8\sqrt3$$, which is your final answer.

Nov 4, 2020
#2
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The length of the shortest leg = [sqrt(162 - 82)] / 2

Nov 4, 2020