Understanding Right-Angled Triangles
In a right-angled triangle, the sides are classified as follows:
- Opposite Side: The side opposite the angle you're interested in (1 cm in this case).
- Adjacent Side: The side next to the angle you're interested in (also 1 cm here).
- Hypotenuse: The longest side of the triangle, opposite the right angle.
Using the Pythagorean Theorem
To find the hypotenuse (c) when you know the lengths of the opposite (a) and adjacent (b) sides, you can use the Pythagorean theorem. This theorem states that:
- c² = a² + b²
Here, a and b are the lengths of the two shorter sides of the triangle.
Calculating the Hypotenuse
Let’s calculate using the given values:
- Opposite Side (a): 1 cm
- Adjacent Side (b): 1 cm
Now plug these values into the formula:
1. Square the lengths of the opposite and adjacent sides:
- a² = 1² = 1
- b² = 1² = 1
2. Add these squared values:
- a² + b² = 1 + 1 = 2
3. Find the square root to get the hypotenuse:
- c = √(2)
Thus, the hypotenuse (c) is approximately 1.41 cm.
Conclusion
To summarize, when both the opposite and adjacent sides of a right-angled triangle measure 1 cm, the hypotenuse can be found using the Pythagorean theorem, resulting in a length of approximately 1.41 cm.