To find the distance of the sailboat from the port after moving 12 kilometers west and 9 kilometers north, we can use the Pythagorean Theorem.
1. Start by drawing a diagram where you have a right-angled triangle representing the sailboat's path.
2. Label the sides of the triangle: the 12-kilometer side as the base (west), the 9-kilometer side as the height (north), and the distance from the port as the hypotenuse.
3. Apply the Pythagorean Theorem which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): \(c^2 = a^2 + b^2\).
Now, substitute the values into the formula:
\(c^2 = 12^2 + 9^2\)
\(c^2 = 144 + 81\)
\(c^2 = 225\)
To find the length of the hypotenuse (c), take the square root of 225:
\(c = \sqrt{225}\)
\(c = 15\) kilometers
Therefore, the sailboat is 15 kilometers away from the port after moving 12 kilometers west and 9 kilometers north.
