Question

WILL MARK BRAINLIEST!

Answer 1

Answer:

Following are the responses to the given points:

Step-by-step explanation:

Dilation implies the triangle $\Delta XYZ$ stretched through the factor "2".  

$m\angle Y = m\angle C = 90^{\circ} \leftarrow given$  

right triangles:

$\Delta XYZ and \Delta ACB \\\\\angle X \cong \angle A \leftarrow given$

complementary angles:  

$\angle X \ and\ \angle Z$

$m\angle Z = 90^{\circ} - m\angle X$

complementary angles:

$\angle A \ and\ \angle B$

$m\angle B = 90^{\circ} - m\angle A \\\\\therefore \\\\ \angle Z \cong \angle B \\\\\Delta XYZ \sim \Delta ACB$

Same triangles: proportional side are corresponding, congruence angles are respective.

$\sin \angle X = \frac{5}{5.59} \leftarrow given \\\\\sin\angle X = \frac{YZ}{XY} \\\\YZ = 5 (units) \rightarrow leg in \Delta XYZ \\\\XZ = 5.59 (units) \rightarrow hypotenuse \ in\ \Delta XYZ$

Calculating the length of leg XY:

$XY = \sqrt{((5.59)^2 - 52)} \cong 2.4996 (units)\\\\\frac{CB}{YZ} = 2 \leftarrow given \\\\CD = 2YZ = 2 \times 5 = 10 \ (units)\\\\\frac{AC}{XY} = 2 \leftarrow \ given\\\\AC = 2XY \cong 2 \times 2.4996 \cong 4.999\ (units)$