Final answer:
To find the value of x, the leg of the right triangle, we use the cosine function with angle 27 degrees and hypotenuse 64 km. After calculating, we find that x is approximately 57.3 km, which does not match any of the given options.
Step-by-step explanation:
The value of x in the given right triangle can be found using trigonometric functions. Considering the angle given is 27 degrees and the hypotenuse is 64 kilometers, we can use the cosine function, which relates the adjacent leg (our unknown x) to the hypotenuse in a right triangle. The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse.
Using the formula:
cos(27°) = x / 64 km
We can rearrange the equation to solve for x:
x = cos(27°) × 64 km
Calculating this gives us:
x = cos(27°) × 64 km ≈ 57.3 km
When rounded to the nearest tenth, the value of x is 57.3 km, so none of the options given (a, b, c, d) are correct.