Final answer:
To determine the distance Ava needs to travel to reach the camp, we use the Pythagorean theorem. By calculating the hypotenuse of the right triangle formed by Ava and Presley's paths, we find that Ava needs to travel approximately 28 meters to reach the camp.
Step-by-step explanation:
The question provided asks to find the distance Ava needs to travel in order to reach Presley at the camp, starting from a different point in the woods. Since Presley ran 24 meters North and Ava ran 16 meters West from the same starting point, we can use the Pythagorean theorem to find the distance between Ava's current position and the camp. This forms a right triangle with the legs being 24 meters and 16 meters, respectively.
Step-by-step Solution:
- Identify the two legs of the right triangle formed by the paths of Presley and Ava. Presley's path is one of the legs, measuring 24 meters to the north (vertical leg). Ava's path is the other leg, measuring 16 meters to the west (horizontal leg).
- Apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs). This is expressed as c2 = a2 + b2.
- Calculate the hypotenuse by substituting the given values into the formula: c2 = 242 + 162.
- Perform the calculations to find the square of the hypotenuse: c2 = 576 + 256, which equals 832.
- Take the square root of 832 to find the length of the hypotenuse: c is approximately 28.84 meters. Since we only have whole numbers as answer choices, we round this to 28 meters.
- Therefore, the distance Ava needs to travel is 28 meters to reach the camp, which corresponds to option C).