Final answer:
Using the cosine function cos(16°) = DE / 65, we find that DE is approximately 62.5 feet to the nearest tenth.
Step-by-step explanation:
To find the length of DE, we can use trigonometric functions, specifically the cosine function, since we have an angle and the hypotenuse of a right triangle ECDE with ∠E being 90° and ∠C being 16°. The length of DE represents the adjacent side to ∠C, and EC is the hypotenuse.
The formula using the cosine function is:
cos(C) = adjacent / hypotenuse
Plugging in the values we have:
cos(16°) = DE / 65 feet
Now we can solve for DE:
DE = 65 feet * cos(16°)
Calculating this using a calculator:
DE ≈ 65 feet * 0.9613 ≈ 62.4845 feet
Round to the nearest tenth:
DE ≈ 62.5 feet
Therefore, the length of DE to the nearest tenth of a foot is 62.5 feet.