Consider a map oriented so that the x-axis runs east-west (with east being the "positive" direction) and y runs north-south (with north "positive"). A person drives 23 km to the north, turns and drives 76 km to the east, and then turns north and drives for an unknown distance z. If his final position is 92 km from where he started, find z.


Find:

__________ km

67

To find the value of z, let's analyze the given information step by step.

1. The person drives 23 km to the north, which means they move up in the positive y direction. Let's denote this as a positive change in position: Δy = 23 km.

2. The person then turns and drives 76 km to the east, which means they move to the right in the positive x direction. This can be denoted as a positive change in position: Δx = 76 km.

At this point, we can calculate the total distance travelled by using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

The total distance travelled from the starting point can be calculated using the formula:

Distance^2 = Δx^2 + Δy^2

Substituting the given values:

92^2 = (76)^2 + (23)^2

8464 = 5776 + 529

8464 = 6305

This equation is not possible, which means there might be a mistake in the given information or in the calculations.

Please double-check the distances or values provided, as the current information does not lead to a valid solution for z.