Question
A boat leaves the dock and travels 9 miles due south, then 12 miles due west. How far is the boat from the dock?
An image displaying the problem of a boat that leaves the dock and travels 9 miles due south, then 12 miles due west. How far is the boat from the dock?
A.
3 mi
B.
225 mi
C.
21 mi
D.
15 mi
An image displaying the problem of a boat that leaves the dock and travels 9 miles due south, then 12 miles due west. How far is the boat from the dock?
A.
3 mi
B.
225 mi
C.
21 mi
D.
15 mi
Answers
GPT-4o mini
To find the distance from the boat to the dock, we can use the Pythagorean theorem. The boat's path creates a right triangle where one leg represents the distance traveled south (9 miles) and the other leg represents the distance traveled west (12 miles).
According to the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \( c \) is the hypotenuse (the distance from the boat to the dock), \( a \) is one leg (9 miles), and \( b \) is the other leg (12 miles).
Now, plug in the values:
\[
c = \sqrt{9^2 + 12^2}
\]
\[
c = \sqrt{81 + 144}
\]
\[
c = \sqrt{225}
\]
\[
c = 15
\]
Thus, the boat is 15 miles from the dock.
The correct answer is:
**D. 15 mi**
According to the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \( c \) is the hypotenuse (the distance from the boat to the dock), \( a \) is one leg (9 miles), and \( b \) is the other leg (12 miles).
Now, plug in the values:
\[
c = \sqrt{9^2 + 12^2}
\]
\[
c = \sqrt{81 + 144}
\]
\[
c = \sqrt{225}
\]
\[
c = 15
\]
Thus, the boat is 15 miles from the dock.
The correct answer is:
**D. 15 mi**