Final answer:
Using the cosine function of angle N, NO is calculated to be approximately 36.7 feet, but this answer is not among the provided options, indicating an error in the question or the options.
Step-by-step explanation:
To find the length of NO in triangle AMNO where angle O is 90°, angle N is 37°, and OM is 46 feet, we can use trigonometric functions. Because angle O is 90°, triangle AMNO is a right triangle and we can use the function cosine for angle N to solve for NO:
cos(N) = Adjacent/Hypotenuse
cos(37°) = NO/OM
cos(37°) = NO/46
NO = 46 × cos(37°)
Now, we calculate the value of cos(37°) and multiply it by 46 feet to find NO:
NO = 46 × 0.7986 (cosine of 37° rounded to four decimal places)
NO = 36.7356 feet
Rounding to the nearest tenth of a foot, NO is approximately 36.7 feet. Hence, the answer closest to our calculation is not listed among the provided options a. 34.3 feet, b. 53.7 feet, c. 68.4 feet, d. 81.1 feet, indicating a potential error in the question or the options given.