Final answer:
If the legs are 9 and 5, the hypotenuse is approximately 10.3.
Step-by-step explanation:
The Pythagorean theorem is a fundamental principle in Mathematics that defines the relationship between the sides of a right-angled triangle. This relationship is expressed as a² + b² = c², where a and b are the lengths of the triangle's legs and c is the length of the hypotenuse. When calculating the missing side of a right triangle, if the lengths of the two legs (a and b) are known, the hypotenuse (c) can be found using the equation c = √(a² + b²). Conversely, if one leg and the hypotenuse are known, the other leg can be found by rearranging the equation accordingly. For instance, if the lengths of the legs are 9 and 5, the length of the hypotenuse can be calculated as follows:
- c = √(9² + 5²)
- c = √(81 + 25)
- c = √106
- c = √(2··53) -- Further simplification in radical form
- c = √2·√53
- c = √2×√53
- c = √2 × 7.29 (approximation)
- c = 1.41 × 7.29
- c ≈ 10.3 (approximation)