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

1/2*qr*rs

step-by-step explanation: