Triangle XYZ was dilated by a scale factor of 2 to create triangle ABC and cos X = 2.5/5.59 PART A: Yse complete sentences to explain the special relationship between the trigonometric Ratios of triangles XYZ and ABC

PART B: Explain how to find the measures of segments AC and BC.

A) The trigonometric ratios are the same for both triangles because they are similar

B) AC = 5, BC = 10

Step-by-step explanation:

A) Given that triangle XYZ was dilated by a scale factor of 2 to create triangle ABC, then:

∠A ≅ ∠X

By definition:

cos ∠X = adjacent/hypotenuse

cos ∠X = XY/XZ

and

cos ∠A = AC/AB

but AC = 2*XY and AB = 2*XZ, then:

cos ∠A = (2*XY)/(2*XZ) = XY/XZ = cos ∠X

The same is valid for all trigonometric ratios

B) cos ∠X = XY/XZ = 2.5/5.59

therefore, XY = 2.5 and XZ = 5.59

AC = 2*XY = 2*2.5 = 5

and

AB = 2*XZ = 2*5.59 = 11.18

From Pythagorean theorem:

AC² + BC² = AB²

BC = √(AB² - AC²)

BC = √(11.18² - 5²)

BC = 10

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step-by-step explanation:

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.