Final answer:
The expression to find the hypotenuse c in a right-angled triangle where the lengths of the other two sides a and b are known is c = √(a² + b²) according to the Pythagorean theorem.
Step-by-step explanation:
To find the value of the hypotenuse c in a right triangle where the sides opposite and adjacent to the acute angle are known, we use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Specifically, the relationship is given by the equation a² + b² = c².
In the case of a right triangle with a 45-degree angle, if one side is a and the other side is b, both of which are the legs of the triangle, and given that this triangle conforms to the characteristics of a right triangle, we can find c by rearranging the theorem to solve for the hypotenuse:
c = √(a² + b²)
This expression allows us to calculate the length of the hypotenuse if we know the lengths of the other two sides. It's also useful to remember that in a right triangle with a 45-degree angle, the lengths of the two legs are equal if the angles opposite them are also 45 degrees (a = b). However, since the question specifies that a and b are different, we will not assume they are equal here.