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Chapter 4: Problem 15

A ship sails north for 2 miles and then west for 5 miles. How far is the ship from its starting point?

Short Answer

Expert verified
The ship is approximately \(\sqrt{29}\) miles from its starting point.

Step by step solution

01

Identify the given information

The ship sails 2 miles north (in the vertical direction) and 5 miles west (in the horizontal direction). This information represents the lengths of the legs in a right triangle.
02

Draw the right triangle

In order to visualize the concept, draw a right triangle in which one leg is vertical (representing the 2-mile distance the ship sails north) and the other leg is horizontal (representing the 5-mile distance the ship sails west). The hypotenuse represents the straight-line distance between the ship's starting point and its current location.
03

Apply the Pythagorean theorem

Using the Pythagorean theorem, calculate the square of the length of the hypotenuse by adding the squares of the lengths of the legs of the right triangle together. Let the distance between the starting point and the ship's current location be represented as D. Then, \[D^2 = 2^2 + 5^2\]
04

Evaluate the expression

Next, calculate the sum of the squares of the lengths of the legs of the right triangle: \[D^2 = 2^2 + 5^2 = 4 + 25 = 29\]
05

Find the length of the hypotenuse

Finally, find the length of the hypotenuse (the straight-line distance between the ship's starting point and its current location) by taking the square root of the value obtained in Step 4: \[D = \sqrt{29}\]
06

Express the answer in terms of distance

The ship is approximately \(\sqrt{29}\) miles from its starting point. This is the final answer.

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