Final answer:
Jane is approximately 18.0 miles from her house after traveling 15 miles west and then 10 miles south, as calculated using the Pythagorean theorem.
Step-by-step explanation:
Jane takes a boat 15 miles west and then 10 miles south. To find out how far away from home she is, we can use the Pythagorean theorem since her path forms a right triangle. The distance from home is the hypotenuse of the right triangle where the legs are the westward and southward trips.
The steps to solve the problem are as follows:
- Identify the lengths of the two legs of the triangle. The westward trip is one leg and is 15 miles long, and the southward trip is the other leg and is 10 miles long.
- Apply 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): a² + b² = c².
- Substitute the lengths of the legs into the theorem: 15² + 10² = c², which gives 225 + 100 = c².
- Solve for c by taking the square root of the sum of the squares of the legs: √(225 + 100) = √325 ≈ 18.0277563773.
- Round the result to the nearest tenth of a mile to find that Jane is approximately 18.0 miles from her house