Final answer:
Claude is approximately 45.49 miles from his starting point after traveling due south for 38 miles and then due west for 25 miles. This is calculated using the Pythagorean theorem to find the hypotenuse of the right-angled triangle formed by his path.
Step-by-step explanation:
The question about Claude sailing his boat deals with the concept of vector addition and the Pythagorean theorem in mathematics. The student wants to find out how far Claude is from his starting point after traveling south and then west. Since these directions are perpendicular to each other, the path forms a right-angled triangle. The required distance is the hypotenuse of this right-angled triangle.
To find this distance, we use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Thus, the formula is:
c = √(a² + b²)
Plugging in the values from the question:
- a = 38 miles (south)
- b = 25 miles (west)
The hypotenuse (c) is:
c = √(38² + 25²) = √(1444 + 625)
= √2069
Calculating this, we get:
c ≈ √2069
≈ 45.49 miles
Therefore, Claude is approximately 45.49 miles from where he began.