Explain pythogaras theorem
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Step-by-Step Solution
Step 1: State the Theorem
The 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. Here, a and b are the lengths of the two shorter sides (legs), and c is the length of the hypotenuse.
Step 2: Identify Sides of a Right Triangle
Consider a right-angled triangle. One angle measures 90∘. The side opposite this right angle is always the longest side, known as the hypotenuse (c). The other two sides are called legs (a and b).
Step 3: Apply to an Example
Let's take an example where the lengths of the two legs are a=3 units and b=4 units. We want to find the length of the hypotenuse, c.
Step 4: Substitute Values into the Formula
Substitute the values of a and b into the Pythagorean theorem formula. This sets up the equation we need to solve for c.
Step 5: Calculate the Squares
First, calculate the squares of the given leg lengths. 32=3×3=9 and 42=4×4=16. Then, sum these values.
Step 6: Sum the Squared Lengths
Add the squared values together: 9+16=25. This result represents the square of the hypotenuse length, c2.
Step 7: Find the Hypotenuse Length
To find the length of c, take the square root of 25. Since length must be positive, we take the positive square root. The hypotenuse c is 5 units long.