Understanding Pythagoras' Theorem
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is mathematically expressed as:
c² = a² + b²
Where:
- c = length of the hypotenuse
- a = length of one side
- b = length of the other side
Identifying the Sides
- To apply this theorem, first identify the sides of your triangle:
- Hypotenuse (c): The longest side opposite the right angle.
- Legs (a and b): The other two sides that form the right angle.
Solving for Unknown Sides
- If you know the lengths of two sides, you can find the third side:
- Example: If a = 3 and b = 4, find c.
- Calculate: c² = 3² + 4²
- This gives c² = 9 + 16 = 25
- Therefore, c = √25 = 5
Finding Missing Lengths
- If you need to find one of the legs:
- Rearrange the formula: a² = c² - b²
- Example: If c = 10 and b = 6, find a.
- Calculate: a² = 10² - 6²
- This gives a² = 100 - 36 = 64
- Therefore, a = √64 = 8
Practical Applications
- Pythagoras' Theorem is useful in various real-life scenarios, including:
- Calculating distances
- Designing structures
- Navigation and map reading
By understanding and applying these principles, solving problems related to right-angled triangles becomes straightforward!