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Introduction

In this tutorial, we will determine the distance between two cars observed by two individuals, A and B. A is located at a distance of 34 meters from one car, while B is 52 meters away from another car. This problem involves basic geometry and the application of the Pythagorean theorem to find the distance between the two cars.

Step 1: Understand the Problem

• Identify the Positions:
  • A is 34 meters away from Car 1.
  • B is 52 meters away from Car 2.
• Visualize the Scenario:
  • Imagine a right triangle where one leg represents the distance from A to Car 1 and the other leg represents the distance from B to Car 2.

Step 2: Set Up the Right Triangle

• Label the Triangle:
  • Let point A represent the location of observer A.
  • Let point B represent the location of observer B.
  • Let point C represent Car 1 and point D represent Car 2.
• Establish the Distances:
  • Distance AC = 34 m (from A to Car 1).
  • Distance BD = 52 m (from B to Car 2).

Step 3: Apply the Pythagorean Theorem

• Formula: The Pythagorean theorem states that in a right triangle:

  [ c^2 = a^2 + b^2 ]

  Where:

  • c is the distance between the two cars.
  • a is the distance from A to Car 1 (34 m).
  • b is the distance from B to Car 2 (52 m).

• Calculation:

  • Substitute the values into the equation:

  [ c^2 = 34^2 + 52^2 ]

• Perform the Squaring:

  • ( 34^2 = 1156 )
  • ( 52^2 = 2704 )

• Add the Squared Values: [ c^2 = 1156 + 2704 = 3860 ]

• Calculate c: [ c = \sqrt{3860} \approx 62.1 \text{ meters} ]

Step 4: Interpret the Result

• Conclusion of Calculation: The distance between the two cars is approximately 62.1 meters.
• Practical Application: This calculation can be used in various scenarios, such as determining safe distances for parking or analyzing visibility in traffic scenarios.

Conclusion

In this tutorial, we successfully calculated the distance between two cars observed by two individuals using basic geometry and the Pythagorean theorem. The key takeaway is that by visualizing the scenario and applying the theorem correctly, we can solve problems involving distances in a clear and structured manner. For further practice, you can try similar problems involving different distances or angles to enhance your understanding of geometry.