on a drive through allegheny county, natalie drove due west for 9 miles, then turned left and proceeded to drive due south. after traveling 12 miles south, what was the straight line distance between where natalie started and where she ended her drive?

Question

on a drive through allegheny county, natalie drove due west for 9 miles, then turned left and proceeded to drive due south. after traveling 12 miles south, what was the straight line distance between where natalie started and where she ended her drive?

A 13 miles

B 14 miles

C 15 miles

D 16miles

E 21 miles

I picked C. If someone can correct me on the right answer.

Answer 1

correct. It's just a 3-4-5 right triangle, scaled up by 3.

Answer 2

To find the straight line distance between where Natalie started and where she ended her drive, we can use the Pythagorean theorem.

First, let's consider the 9-mile drive due west. This creates the base of a right triangle.

Next, let's consider the 12-mile drive due south. This creates the height of the right triangle.

Using the Pythagorean theorem, we can find the hypotenuse, which represents the straight line distance between Natalie's starting and ending points.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, the formula is:

c² = a² + b²

where a = 9 miles and b = 12 miles.

c² = 9² + 12²
c² = 81 + 144
c² = 225

Taking the square root of both sides, we get:

c = √225
c = 15

Therefore, the straight line distance between where Natalie started and where she ended her drive is 15 miles.

So, the correct answer is C) 15 miles.

Answer 3

To find the straight line distance between where Natalie started and where she ended her drive, we can use the Pythagorean theorem.

First, let's consider Natalie's movement. She first drove due west for 9 miles. Then she turned left and drove due south for 12 miles.

Since she drove 9 miles due west and then 12 miles due south, we have a right-angled triangle. The distance between where she started and where she ended is the hypotenuse of this right triangle.

Using the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore:
Hypotenuse^2 = (9^2) + (12^2)
Hypotenuse^2 = 81 + 144
Hypotenuse^2 = 225

Now, let's find the square root of 225 to get the length of the hypotenuse:
Hypotenuse = √225
Hypotenuse = 15

So, the straight line distance between where Natalie started and where she ended her drive is 15 miles.

Therefore, the correct answer is C) 15 miles.