Final answer:
To find the length of segment CA, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. By plugging in the given values, we can solve for CA and find that its length is approximately 12.806 units.
Step-by-step explanation:
The length of segment CD is 8 units and the length of the segment CB is 10 units. To find the length of segment CA, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Segment CA is the hypotenuse and segments CD and CB are the other two sides. So, we can write the equation as:
CA2 = CD2 + CB2
Plugging in the given values, we have:
CA2 = 82 + 102
Simplifying the equation gives:
CA2 = 64 + 100
CA2 = 164
Taking the square root of both sides gives:
CA ≈ √164
CA ≈ 12.806
So, the length of segment CA is approximately 12.806 units.