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?

Guest Nov 8, 2020

#1**+2 **

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)

hectictar Nov 8, 2020