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 12 miles line distance between where natalie startd and where she ended her drive? 1] 13 miles 2] 14 miles 3] 15 miles 4] 16 miles 5]21 miles help please

Pythagorean Theorem:

a^2 + b^2 = c^2

9^2 + 12^2 = c^2

81 + 144 = c^2

225 = c^2

15 = c

You're welcome.

Well, if Natalie drove due west for 9 miles and then turned left to drive due south for 12 miles, we can use the Pythagorean theorem to find the straight-line distance between where she started and where she ended.

First, let's draw it out. We have a right-angled triangle with one side measuring 9 miles (from her starting point to where she made the left turn) and another side measuring 12 miles (from where she made the left turn to where she ended her drive).

Now, let's use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.

So, using the formula: a^2 + b^2 = c^2, where a = 9 and b = 12, we can find the straight-line distance (c).

9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2

Now take the square root of both sides:
√225 = √c^2
15 = c

So the straight 12-mile line distance between where Natalie started and where she ended her drive is 15 miles!

So the answer is 3] 15 miles.

Hope that gave you a mathematical giggle!

thanks

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 visualize the path Natalie took: Natalie initially drove due west for 9 miles, and then turned left (which means she turned 90 degrees counterclockwise) and drove due south for 12 miles.

The two sides of the resulting right triangle represent the distances traveled west and south. The hypotenuse of this triangle represents the straight-line distance between the starting and ending points.

Using the Pythagorean theorem, we can determine the length of the hypotenuse:

c² = a² + b²,

where c is the hypotenuse and a and b are the two sides.

In this case, a = 9 miles and b = 12 miles, so we have:

c² = 9² + 12²,
c² = 81 + 144,
c² = 225.

Taking the square root of both sides, we find:

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 option 3) 15 miles.