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 longer leg of the smaller triangle?
Let's find the longer leg of the larger triangle first ...this is also the hypotenuse of the smaller triangle
cos 30 = sqrt3 / 2 = adj / hyp = adj/16
adj = 16 sqrt3 / 2 = 8 sqrt3 = hypotenuse of smaller triangle
now for the smaller triangle
cos 30 = adj / hyp = sqrt 3 / 2 = adj / (8 sqrt 3)
adj = longer leg = sqrt 3 / 2 * 8 sqrt 3 = 12 cm