Studyfin
✨ Sign up free
Hey there! Ready to discover one of the most famous and useful secrets in geometry? Let's explore how the sides of a right-angled triangle work together like magic!
Every triangle has three sides, but right-angled triangles have a special superpower. A right-angled triangle is any triangle that has one perfect 'square corner' measuring exactly 90 degrees.
The two sides that meet to form the 90-degree corner are called the 'legs'. The longest side, which sits directly opposite the right angle, is called the 'hypotenuse'. We usually label the legs 'a' and 'b', and the hypotenuse 'c'.
The Greek philosopher Pythagoras discovered that if you build a square on each of the three sides, the areas of the two smaller squares (a² and b²) add up exactly to the area of the largest square (c²). This gives us our golden formula: a² + b² = c²!
A right-angled triangle has a vertical leg of length 3 cm and a horizontal leg of length 4 cm. Find the length of the hypotenuse (c).
- Identify your given values: leg a = 3 and leg b = 4.
- Write down the Pythagorean formula: a² + b² = c².
- Plug in the numbers: 3² + 4² = c².
- Calculate the squares: 9 + 16 = c², which simplifies to 25 = c².
- Find the square root of both sides to get c: √25 = 5.
- The length of the hypotenuse is 5 cm!
