the answer is in the question plz help!! thank you!!!

Question

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan ∠X = .

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)

Answer 1

OK, so every side in triangle XYZ is twice as long as the corresponding side in ABC:

XY = 2AB

XZ = 2AC

YZ = 2AC

The angles, however, are the same:

m∠A = m∠X

m∠B = m∠Y

m∠C = m∠Z

Let's look at the sine function:

sin A = opposite/hypotenuse = BC/AB

sin X = opposite/hypotenuse = YZ/XY = 2BC/2AB = BC/AB = sin A

So sin X = sin A. The same is true for all of the trig functions. Try it for the cosine and tangent functions. The value of the trig functions depends only on the angle and not on the size of the triangle.