Mrs.Culowski traveled 24.0 kilometers north and then 10.0 kilometers east. How far was she from her starting point?

use pytheorn Theorm

i need help seting up the problem?

a^2 + b^2 = c^2

24^2 + 10^2 = c^2

To solve this problem using the Pythagorean theorem, we need to set up a right triangle. Let's assume Mrs. Culowski's starting point is the vertex of the right angle (point A), and her final location is the endpoint of the triangle's hypotenuse (point B).

Since she traveled 24.0 kilometers north, we can draw a vertical line segment from point A to point B, which represents the northward direction. The length of this line segment is 24.0 kilometers.

Similarly, since she traveled 10.0 kilometers east, we can draw a horizontal line segment from point A to point B, which represents the eastward direction. The length of this line segment is 10.0 kilometers.

Now, we can label the vertical line segment as 'a' (length of 24.0 kilometers) and the horizontal line segment as 'b' (length of 10.0 kilometers). The length of the hypotenuse (c) can be calculated using the Pythagorean theorem as follows:
c^2 = a^2 + b^2

Let's substitute the values into the formula and solve for c:
c^2 = 24.0^2 + 10.0^2
c^2 = 576.0 + 100.0
c^2 = 676.0

To find the value of c, we can take the square root of both sides:
c = √676.0
c ≈ 26.0 kilometers

Therefore, Mrs. Culowski was approximately 26.0 kilometers away from her starting point.