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 =
=
Cos X =
Tan 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
