Explain Pythagoras theorem to me
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Step-by-Step Solution
Step 1: Understand the Right-Angled Triangle
The Pythagorean theorem applies specifically to right-angled triangles. A right-angled triangle is a triangle that has one angle measuring exactly 90 degrees. The side opposite the right angle is called the hypotenuse, which is always the longest side. The other two sides are called the perpendicular and the base.
Step 2: State the Pythagorean Theorem
The Pythagorean theorem states that in a right-angled 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. If we label the hypotenuse as c and the other two sides as a and b, the theorem can be written as c2=a2+b2.
Step 3: Apply the Theorem: Example
Let's consider an example. If a right-angled triangle has sides of length 3 units and 4 units, we can find the length of the hypotenuse using the theorem. Substitute a=3 and b=4 into the formula.
Step 4: Calculate the Hypotenuse
First, square the lengths of the two shorter sides: 32=9 and 42=16. Then, add these squares together: 9+16=25. Finally, take the square root of the sum to find the length of the hypotenuse: 25=5. So, the hypotenuse is 5 units long.