Dilation is the process in which the dimensions of a given shape is increased or decreased by a scale factor. Therefore the answers to the questions are:

A. Since the dilation of triangle XYZ do not affect the measure of its internal angles, then the trigonometric ratios of respective internal angles are the same.

B. segment CB = 10

ii. segment AB = 11.18

From the given information in the question, triangle XYZ is an image of triangle ACB. In triangle XYZ, given that Sin X = ; it implies that its hypotenuse is 5.59, and the opposite side as 5. So that;

Sin X =

X = 0.8945

X =

Thus,

<X + <Y + <Z =

+ + <Z =

<Z = -

<Z =

So then, the third side can be determined by applying the Pythagoras theorem.

= +

= -

= 6.2481

x =

= 2.49962

x = 2.5

Thus,

Cos X =

Tan X =

Therefore:

A. Considering triangles XYZ and ACB, the measure of their respective internal angles are the same.

i.e <X ≅ <A

<B ≅ <Z

<C ≅ <Y

So that the trigonometric ratios of respective internal angles are the same.

B. Given that triangle XYZ was dilated by a scale factor of 2, then the respective length of each sides of triangle ACB is twice that of XYZ.

Then,

i. segment CB = 2 x segment YZ

= 2 x 5

segment CB = 10

ii. segment AB = 2 x segment XZ

= 2 x 5.59

segment AB = 11.18

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3 years ago