1) Considering that the dilation made two similar triangles: angles are congruent and the length of their sides are proportional.
Part A)
Since the
[tex]\begin{gathered} \sin (X)\text{ =}\frac{5}{5.59} \\ \sin (X)=0.894 \\ X\text{ = }\sin ^{-1}(0.894) \\ X\approx63.38^{\circ} \end{gathered}[/tex]
We can write for the sine (A), given the scale factor k=2:
[tex]\begin{gathered} \sin (A)\text{ =}\frac{10}{11.18} \\ \sin \text{ (A) =0.894} \\ (A)\approx\text{ 63.38º} \end{gathered}[/tex]
Therefore we can prove both triangles are similar
Part B)
To find out the measures of segment CB and AB, based on what we already know of triangle ABC
So since the dilation is k=2, all sides of ABC are twice larger in comparison to XYZ, as the formula of the sine relates the opposite leg to angle A and the hypotenuse, then we can write:
BC = (5x 2)=10
AB=(5.59 x 2) = 11.18
