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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 largest triangle is 8 centimeters. What is the number of centimeters in the length of the shorter leg of the smallest triangle?

 

 Nov 8, 2020
 #1
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The side across from the 60° angle is √3 times the side across from the 30° angle,

and the side across from the 30° angle is half the hypotenuse.  So...

 

a   =   8/2 * √3   =   4√3

 

b   =   a/2 * √3   =   4√3 / 2  *  √3   =   2√3 * √3   =   2 * 3   =   6

 

c   =   b/2 * √3   =   6/2 * √3   =   3√3

 

d   =   c/2   =   3√3 / 2

 

(where a, b, c, and d are all in cm)

 Nov 8, 2020

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