Explain pythogaras theorem to me
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Step-by-Step Solution
Step 1: Define the 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. This fundamental theorem is used to find an unknown side length of a right triangle or to determine if a triangle is a right triangle.
Step 2: Identify Sides of a Right Triangle
To apply the theorem, first identify the right angle in the triangle. The side directly opposite this angle is always the hypotenuse, labeled as c. The other two sides are called the legs, typically labeled as a and b. It doesn't matter which leg is a and which is b.
Step 3: Example Application
Let's consider a practical example. If we have a right triangle with legs of length 3 units and 4 units, we can use the Pythagorean Theorem to find the length of the hypotenuse. We substitute the known values of a and b into the formula.
Step 4: Substitute and Calculate
Substitute the values a=3 and b=4 into the equation a2+b2=c2. Calculate the squares of the leg lengths, sum them up, and then take the square root of the result to find the length of the hypotenuse, c. In this case, the hypotenuse is 5 units long.