Question

A boat leaves a dock and travels 9 miles due north and 12 miles due west. Find how far the boat is from the dock. Type the correct answer: ____miles

Answer 1

15 miles

Explanation:

This path forms a right angle triangle

Required distance is the

hypotenuse

sqrt(9² + 12²)

sqrt(225)

15

Answer 2

15 miles

Explanation:

Let's say the dock is at the origin on a coordinate plane and each unit is 1 mile. If the boat travels 9 mile due north, that means that we move up from the origin (0, 0) 9 units to point A (0, 9). Now, this boat moves 12 miles due west, so we will go 12 units to the left of (0, 9) to point B (-12, 9). See the attached drawing (sorry for the crudeness).

Notice that this is a right triangle with legs of 9 and 12. That means the distance from the boat to the dock is just the hypotenuse, so use the Pythagorean Theorem: distance =
`√(9^2+12^2) =√(81+144) =√(225) =15`

Thus, the answer is 15 miles.

Hope this helps!