Final answer:
The length of AB in a right triangle can be found using the Pythagorean theorem, solving for b given a=3 and c=4 by computing b = √(4^2 - 3^2), which results in b = √7.
Step-by-step explanation:
The length of AB in a right triangle can be found using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). According to the equation provided, 32 + b2 = 42, we are given the lengths of one leg (a=3) and the hypotenuse (c=4) of a right triangle and asked to find the length of the other leg (b).
To find the length of AB, or 'b' in this context, we rewrite the equation to solve for b2: b2 = 42 - 32. Taking the square root of both sides gives us b = √(42 - 32). Therefore, to find the length of AB, we calculate b = √(16 - 9), which simplifies to √7.