The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where
<h3>What is the dilation about?</h3>
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.
Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:
tanX = tanA = 5 over 2 and 5 tenths
AC = 2 x XY
CB = 2 x YZ
Another way to solve for it is by:
Note that Dilation of the triangle ΔXYZ was by a factor of "2".
Since m∠Y = m∠C = 90º - given
ΔXYZ and ΔACB are said to be right triangles.
Since ∠X ≅ ∠A - given
Then ∠X and ∠Z are said to becomplementary angles
Since m∠Z = 90° - m∠X -- given
Then ∠A and ∠B are said to be complementary angles
Since m∠B = 90° - m∠A --- given
Then, ∠Z ≅ ∠B
Therefore ΔXYZ ∼ ΔACB are similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.
Note:
sin ∠X = 5/5.59
sin ∠X = YZ/XY
YZ = 5 seen in ΔXYZ
XZ = 5.59 seen in hypotenuse of ΔXYZ
Then one need to Calculate the length of one aspect of XY:
XY = √((5.59)2 - 52)
= 2.4996
Note CB/YZ = 2
CD = 2*YZ = 2 x 5
= 10
AC/XY = 2
AC = 2* XY
= 2 x 2.4996
= 4.999
Learn more about dilation from:
brainly.com/question/27517432
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