Final answer:
In a right triangle with m∠A = 30° and BC = 6√2, we can solve for the length of AB using the Pythagorean theorem.
Step-by-step explanation:
In a right triangle, the Pythagorean theorem relates the lengths of the legs to the length of the hypotenuse. The relationship is given by the equation a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.
Applying this theorem to the given triangle, where m∠A = 30° and BC = 6√2, we can solve for the remaining side lengths. Let x represent the length of AB. Using the Pythagorean theorem, we have:
(6√2)² + x² = (3x)²
Simplifying the equation, we get:
72 + x² = 9x²
8x² - x² = 72
7x² = 72
x² = 72/7
x = √(72/7)
Therefore, the length of AB is √(72/7).