1.Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2.5/5.59 Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB. You must show all work and calculations to receive full credit.

Step-by-step explanation:

Given

and

See attachment for triangles

Required

Determine the relationship between the trigonometry ratios of both triangles

Using the attachment as a point of reference, we can say that:

implies that:

Because:

Next, is to calculate YZ using Pythagoras theorem.

Collect like terms

Take positive square roots

So, the trigonometry ratio of is:

Given that:

is similar to

This means that:

The following sides are similar

XY and AC; YZ and CB; XZ and AB

And both triangles will have the same trigonometry ratios;

So, the trigonometry ratio of is:

Both ratios can be written together as:

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9