Final answer:
The length of side a in a right triangle with hypotenuse c=22.4 meters and side b=18.2 meters is approximately 13.03 meters, found by applying the Pythagorean theorem.
Step-by-step explanation:
The student is asking to find the length of side a of a right triangle using the Pythagorean theorem. In this theorem, the lengths of the legs of a right triangle (labeled a and b) and the hypotenuse (labeled c) have the relationship: a² + b² = c². If the hypotenuse (c) is 22.4 meters, and one leg (b) is 18.2 meters, we can find a by rearranging the formula: a² = c² - b².
Calculating a, we have:
a² = (22.4 meters)² - (18.2 meters)²
a² = 500.96 meters² - 331.24 meters²
a² = 169.72 meters²
a = √169.72 meters²
a ≈ 13.03 meters
Therefore, the length of side a is approximately 13.03 meters.