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?
It's time for the Pythagorean Theorem! You need to find the hypotenuse of this right triangle.
a^2 + b^2 = c^2
9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2
15 = c
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?
Dhejdje
21 miles
To find the straight line distance between Natalie's starting point and ending point, we can use the Pythagorean theorem.
Let's break down the problem step by step:
1. Natalie drove due west for 9 miles. This establishes the horizontal distance covered.
2. Then, she turned left (which means a 90-degree turn) and proceeded to drive due south for 12 miles. This establishes the vertical distance covered.
By visualizing the path Natalie took, we can see that these two distances, horizontal and vertical, form the sides of a right triangle. The straight line distance between the starting and ending points can be found using the Pythagorean theorem:
c^2 = a^2 + b^2
Where 'c' represents the hypotenuse (the straight line distance), and 'a' and 'b' represent the horizontal and vertical distances, respectively.
In this case:
a = 9 miles (horizontal distance)
b = 12 miles (vertical distance)
Substituting the values into the formula:
c^2 = 9^2 + 12^2
c^2 = 81 + 144
c^2 = 225
Taking the square root of both sides to find 'c':
c = √225
c = 15 miles
Therefore, the straight line distance between where Natalie started and where she ended her drive is 15 miles.