Final answer:
Yes, given two sides of a triangle that measure 3 inches and 4 inches and an included 90° angle, we can form a unique right triangle, as these dimensions satisfy the conditions of the Pythagorean Theorem.
Step-by-step explanation:
The question is related to a concept in mathematics known as triangle formation. If we are given a triangle with two sides measuring 3 inches and 4 inches and they form an included 90° angle, we indeed have enough information to form a right triangle. The reason being is that a triangle is defined as a three-sided figure lying on a plane with three internal angles adding up to 180 degrees. Since we have two sides and the included angle is 90°, we know that the triangle is a right triangle, with the 3-inch and 4-inch sides being the legs of the triangle. According to the Pythagorean Theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, we can conclude that the length of the hypotenuse is 5 inches (since 3² + 4² = 9 + 16 = 25 and √25 = 5). Therefore, we can say that all the necessary conditions for creating a unique right triangle are satisfied.