Using Pythagoras's Theorem to Calculate Missing Lengths in Triangles

Introduction

• The video covers how to use Pythagoras's theorem for finding the missing length in right-angled triangles.

Conditions for Using Pythagoras's Theorem

• Right-Angle Triangle: The triangle must have a 90-degree angle.
• Known Sides: You need to know the lengths of two sides.
• Missing Length: There should be one side whose length is unknown.

Pythagoras's Theorem

• Equation: (a^2 + b^2 = c^2)
  • Important to memorize for problem-solving.
• Designation of Sides:
  • (c) = Hypotenuse (longest side, opposite the right angle).
  • (a) and (b) = Other two sides (interchangeable).

Example Problems

Example 1

• Known Sides: 3 and 4
• Equation Setup:
  • (4^2 + 3^2 = c^2)
  • Simplifies to (16 + 9 = c^2)
  • (25 = c^2)
• Solution:
  • Square root both sides: (c = 5)

Example 2

• Unknown Side: (c)
• Known Sides: 1.7 and 3.2
• Equation Setup:
  • (1.7^2 + 3.2^2 = x^2)
  • Calculator computation: (13.13 = x^2)
• Solution:
  • Square root both sides: (x = 3.62) cm (3 significant figures)

Example 3

• Finding Length: Between points X and Z
• Label Sides: Follow A, B, C labeling to use Pythagoras
• Equation Setup:
  • (5.6^2 + 10.5^2 = c^2)
  • Calculator computation: (141.61 = c^2)
• Solution:
  • Square root both sides: (c = 11.9) cm

Example 4

• Finding Length: Between points A and C
• Equation Setup:
  • (8^2 + 11^2 = c^2)
  • Simplifies to (64 + 121 = c^2)
  • (185 = c^2)
• Solution:
  • Square root both sides: (c = 13.6) cm

Conclusion

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This summary captures the key points and steps for using Pythagoras's theorem to find missing side lengths in right-angled triangles.