PLEASE HELP ! Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin X=5/5.59 Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC you must show all work and calculations to receive full credit. Part B: Explain how to find the measures of segments CB and AB. You must show all work and calculations to receive full credit.

Part A: The corresponding trigonometry ratios of both triangles are equal.

Part B:

CB 10

AB = 5

Step-by-step explanation:

Original image = ∆XYZ

Dilated image = ∆ ACB

Scale factor = 2

Sin X=5/5.59

Find attached the diagram obtained from the given information.

Part A:

Sin X=opposite/hypotenuse = 5/5.59

YZ = 5, XY = 5.59

When a shape is dilated, the new shape has a similar shape but different size.

∆XYZ and ∆ ACB are similar triangles.

AC = scale factor × XY = 2XY

AB = scale factor × XZ = 2XZ

CB = scale factor × YZ = 2YZ

In similar triangles theorem, the ratio of their corresponding sides are equal.

The corresponding trigonometry ratios of both triangles are equal.

Sin X= YZ/XY

Cos X= XZ/XY

Tan X = YZ/XZ

In ∆ACB

Sin A= CB/AC = 2YZ/2XY

Cos A= AB/AC= 2XZ/2XY

Tan A = 2YZ/2XZ

SinA = SinX, CosA = CosX, TanA = TanX

Part B:

To find segment CB, we use the formula relating CB to the corresponding side YZ

CB = scale factor × YZ

CB = 2× 5 = 10

To find segment AB, we use the formula relating AB to the corresponding side XZ

AB = scale factor × XZ

AB = 2× XZ

To get XZ, we use Pythagoras theorem:

XY² = XZ² + YZ²

XZ² = 5.59² - 5²

XZ = √6.2481 = 2.5

AB = 2× 2.5 = 5