The length of the segment CD is 8 units and this can be determined by using the similar triangle property and the Pythagorean theorem.
Given :
- The length of AC = 7 units
- The length of AB = 4 units
- Angle ABC = 90 degrees
- Angle DAC = 90 degrees
The following steps can be used in order to determine the length of the segment CD:
Step 1 - First, determine the length of BC by using the Pythagorean theorem.
[tex]\rm AC^2 = BC^2+AB^2[/tex]
Step 2 - Now, substitute the known values in the above expression.
[tex]\rm 7^2 = BC^2+4^2[/tex]
[tex]\rm BC=\sqrt{49-16}[/tex]
[tex]\rm BC = \sqrt{33}[/tex]
Step 3 - Now, apply the similar triangle property, that is:
[tex]\rm \dfrac{BC}{AC}=\dfrac{AC}{CD}[/tex]
Step 4 - Substitute the values of the known terms in the above expression.
[tex]\rm \dfrac{\sqrt{33} }{7}=\dfrac{7}{CD}[/tex]
[tex]\rm CD=\dfrac{49}{\sqrt{33} }[/tex]
CD = 8 (approximately)
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/25277954
