Final answer:
To determine the length of CD in triangle ACDE, the cosine function was used due to the given angle D and the length of DE. The calculation revealed that CD is approximately 9.5 feet when rounded to the nearest tenth of a foot.
Step-by-step explanation:
To find the length of CD in triangle ACDE where ∠E is 90°, ∠D is 38°, and DE is 12 feet, we can use trigonometric functions. Since we know that DE is the opposite side to ∠D and we are trying to find the length of the adjacent side CD, we can use the cosine function.
The cosine of an angle in a right-angled triangle is equal to the adjacent side divided by the hypotenuse. Using this information:
cos(38°) = CD / DE
Multiplying both sides by DE, we get:
CD = DE * cos(38°)
CD = 12 feet * cos(38°)
Calculating this using a calculator, we find that CD is approximately 9.5 feet, rounded to the nearest tenth of a foot.