(05.01 MC) Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan _X =
5
2.5
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. (5 points)
Part B: Explain how to find the measures of segments AC and CB. You must show all work and
calculations to receive full credit. (5 points)
Source C

When a triangle is dilated (i.e. compressed or enlarged), the size of the new triangle will be different from the original triangle. The special relationship between the trigonometry ratios of both triangles are:

The values of AC and CB are: 5.0 and 10 respectively

The given parameter can be represented as:

The tangent of an angle is:

Using , we have:

By comparison with:

Using Pythagoras theorem, we have:

Substitute known values

Take square roots

Using the following trigonometry formulas:

The trigonometry ratios of angles in are:

Because is similar to then:

To calculate AC and CB, we have the scale factor from to to be 2:

This means that

Sides of = 2 *  Corresponding Sides

So, we have:

and

Learn more dilation at:

x = 12

y = 15

step-by-step explanation: