Teorema Pythagoras [Part 1] - Menentukan Panjang Salah Satu Sisi Pada Segitiga Siku-siku

Introduction

In this tutorial, we will explore the Pythagorean theorem, focusing specifically on how to determine the length of one side of a right triangle. This is particularly useful for students in grade 8 and can be applied in various mathematical and real-world scenarios, such as construction or design.

Step 1: Understanding the Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed with the formula:

c² = a² + b²

Where:

• c is the length of the hypotenuse.
• a and b are the lengths of the other two sides.

Practical Advice

• Always identify the hypotenuse in a right triangle, as this is crucial for applying the theorem correctly.
• Make sure you measure the sides accurately for precise calculations.

Step 2: Determining the Length of One Side

To find the length of one side when the lengths of the other two sides are known, rearrange the formula depending on which side you need to find:

1. Finding the hypotenuse (c):
   • Use the formula:

   c = √(a² + b²)
   

2. Finding one of the legs (a or b):
   • If you need to find side a, rearrange to:

   a = √(c² - b²)
   

   • If you need to find side b, use:

   b = √(c² - a²)
   

Practical Advice

• When subtracting squares, ensure you always subtract the smaller square from the larger square to avoid negative results.
• Use a calculator for square roots to improve accuracy.

Step 3: Example Calculation

Let’s consider an example where you need to find the length of one side:

• Given:

  • Hypotenuse c = 13 cm
  • One side b = 5 cm

• Calculate the length of side a:

a = √(c² - b²)
  = √(13² - 5²)
  = √(169 - 25)
  = √(144)
  = 12 cm

Practical Advice

• Always double-check your calculations to ensure accuracy. You can verify your result by plugging it back into the original formula.

Conclusion

In this tutorial, we covered the fundamentals of the Pythagorean theorem and how to determine the length of a side in a right triangle using the appropriate formulas. Remember to practice with different sets of values to strengthen your understanding.

For further study, consider exploring real-life applications of the Pythagorean theorem, such as in architecture or navigation, to see how this mathematical principle is used in various fields. Keep practicing, and you'll master this essential concept in no time!