Fable :
The Pythagorean theorem is a fundamental principle in geometry that states for 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, called legs. The formula is expressed as \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the lengths of the legs, and \(c\) is the length of the hypotenuse. This theorem is used to find an unknown side length when the other two sides of a right triangle are known. How to use the theorem Identify the sides: In a right-angled triangle, label the two shorter sides (the legs) as \(a\) and \(b\), and the longest side (the hypotenuse) as \(c\). It doesn't matter which leg is labeled \(a\) and which is \(b\). Apply the formula: Plug the known lengths into the formula \(a^{2}+b^{2}=c^{2}\). Solve for the unknown: If you are solving for the hypotenuse (\(c\)), square the lengths of the two legs, add the results, and then find the square root of the sum. If you are solving for one of the legs (e.g., \(a\)), you can rearrange the formula to \(a^{2}=c^{2}-b^{2}\). Then, square the hypotenuse, subtract the square of the known leg, and find the square root of the result. Example Problem: A right triangle has legs of length \(a=3\) and \(b=4\). What is the length of the hypotenuse, \(c\)? Solution: Start with the formula: \(a^{2}+b^{2}=c^{2}\). Substitute the known values: \(3^{2}+4^{2}=c^{2}\). Calculate the squares: \(9+16=c^{2}\). Add the numbers: \(25=c^{2}\). Find the square root of both sides to solve for \(c\): \(c=\sqrt{25}\). The result is \(c=5\). Key takeaways The theorem only applies to right-angled triangles. The formula is \(a^{2}+b^{2}=c^{2}\). \(c\): always represents the hypotenuse, the longest side opposite the right angle. The theorem can be used to find the length of any side of a right triangle if the other two sides are known. Khan Academyhttps://www.khanacademy.orgIntro to the Pythagorean theorem (video) - Khan Academy10:46starclan55. 7 years ago. Posted 7 years ago. Direct link to starclan55's post “When using the Pythagorea...”
2026-03-17 23:14:50