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You start driving east for 12 miles, turn left, and drive north for another 10 miles. At the end of driving, what
is your straight line distance from your starting point? Round to the nearest
tenth of a mile.
Answer Attempt 1 out of 2
mi
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Answer :

Sure! To find the straight-line distance from your starting point to your final point after driving east and then north, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the Problem
You start driving east for 12 miles and then turn left to drive north for 10 miles. We are looking for the straight-line distance from your starting point to the final point. This forms a right-angled triangle where:
- The distance east (12 miles) is one leg of the triangle.
- The distance north (10 miles) is the other leg of the triangle.

### Step 2: Recall the Pythagorean Theorem
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle, which represents our straight-line distance) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this is given by:
[tex]\[ c^2 = a^2 + b^2 \][/tex]

### Step 3: Assign Values
- [tex]\( a = 12 \)[/tex] miles (distance driven east)
- [tex]\( b = 10 \)[/tex] miles (distance driven north)
- [tex]\( c \)[/tex] is the straight-line distance (the hypotenuse) we need to find.

### Step 4: Apply the Pythagorean Theorem
Plug the values into the theorem:
[tex]\[ c^2 = 12^2 + 10^2 \][/tex]
[tex]\[ c^2 = 144 + 100 \][/tex]
[tex]\[ c^2 = 244 \][/tex]
[tex]\[ c = \sqrt{244} \][/tex]

### Step 5: Calculate the Square Root
To find [tex]\( c \)[/tex], take the square root of 244:
[tex]\[ c = \sqrt{244} \approx 15.6205 \][/tex]

### Step 6: Round to the Nearest Tenth
Round [tex]\( 15.6205 \)[/tex] to the nearest tenth:
[tex]\[ c \approx 15.6 \][/tex]

### Conclusion
Your straight-line distance from your starting point, after driving 12 miles east and then 10 miles north, is approximately 15.6 miles.

So, the answer is:
[tex]\[ \text{15.6 miles} \][/tex]