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Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2 and 5 tenths over 5 and 59 hundredths.

Triangles XYZ and ACB; angles Y and C both measure 90 degrees, angles A and X are congruent.
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 AB. You must show all work and calculations to receive full credit. (5 points)

Sagot :

Martebiidn

Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;

Hence:

  • AC = 2 x  XY
  • CB = 2  x YZ

What is the triangle about?

From the question given; Triangle XYZ is known to have been dilated by a scale factor of 2 to form a type of triangle known as triangle  ACB, So therefore, XYZ and ACB are known to be the same or similar triangles.

Since Angles Y and C are known to both measure 90 degrees, and angles A and X are said to be congruent. Therefore:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2  x  XY

CB = 2  x  YZ

For part B:

cosX=Base/Hypotenuse

cos A=AC/AB

AC =  2.05

AB = 5.59

Therefore, Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;

Hence:

  • AC = 2 x  XY
  • CB = 2  x YZ

Learn more about triangles from

https://brainly.com/question/27517432

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