How to Solve for Side A Using the Pythagorean Theorem with Sides 82cm and 18cm

The Pythagorean theorem is used to find the length of a side in a right triangle. It states:

a² + b² = c²

where c is the hypotenuse (the longest side opposite the right angle), and a and b are the other two sides.

Given two sides of 82cm and 18cm, to find side A, first determine if A is a leg or the hypotenuse.

Case 1: Find the hypotenuse (A) when the legs are 82cm and 18cm.

1. Use the formula A² = 82² + 18²
2. Calculate: 82² = 6724 and 18² = 324
3. Add: 6724 + 324 = 7048
4. Take the square root: A = √7048 ≈ 83.9 cm

Case 2: Find a leg (A) when one leg is 18cm and the hypotenuse is 82cm.

1. Use the formula A² + 18² = 82², so A² = 82² - 18²
2. Calculate: 82² = 6724 and 18² = 324
3. Subtract: 6724 - 324 = 6400
4. Take the square root: A = √6400 = 80 cm

Summary:

• If A is the hypotenuse and the other sides are 82cm and 18cm, A ≈ 83.9 cm.
• If A is a leg with hypotenuse 82cm and the other leg 18cm, then A = 80 cm.