The Pythagorean theorem is a fundamental principle in geometry that applies to right-angled triangles. It states that:
a² + b² = c²
where c is the length of the hypotenuse (the side opposite the right angle), and a and b are the lengths of the other two sides.
To find side A, you first need to identify which side A represents:
- If A is one of the legs (a or b):
Rearranging the formula: A = √(c² - other_side²)
- If A is the hypotenuse (c):
A = √(side1² + side2²)
Given the sides provided are 82 cm and 18 cm, let's assume:
- Case 1: 82 cm is the hypotenuse, 18 cm is one leg, find A (the other leg).
- Case 2: 82 cm and 18 cm are legs, find A (the hypotenuse).
Case 1: A is a leg
Use: A = √(c² - b²)
A = √(82² - 18²)
A = √(6724 - 324) = √6400
A = 80 cm
Case 2: A is the hypotenuse
Use: A = √(a² + b²)
A = √(82² + 18²)
A = √(6724 + 324) = √7048
A ≈ 83.91 cm
Summary:
- If 82 cm is the hypotenuse, then side A is 80 cm.
- If 82 cm is a leg, then the hypotenuse A is approximately 83.91 cm.
Make sure you know which side represents the hypotenuse and which sides are the legs before applying the Pythagorean theorem.