Final answer:
The Pythagorean theorem is used to find the length of side ST in a right triangle by taking the square root of the sum of the squares of the other two sides. If ST is the hypotenuse and SR (one leg) and TR (the other leg) are known, use the formula ST = √(SR² + TR²). To find SR, given TR and ST, use SR = √(ST² - TR²).
Step-by-step explanation:
To find the measure of ST in a right triangle TSR, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c). Mathematically, this is represented as a² + b² = c². If ST is the hypotenuse, and we know the lengths of SR and TR, we can solve for ST using the equation ST = √(SR² + TR²). To find the measure of SR to the nearest integer, if TR and ST are known, we rearrange the Pythagorean theorem to solve for SR, obtaining SR = √(ST² - TR²).
To perform these calculations, we need specific values for SR and TR. Since those values were not provided in the question, we will assume generic lengths are given and demonstrate the process. For example, if TR (one leg) is 3 units and SR (the other leg) is 4 units long, the measure of ST (hypotenuse) will be calculated as follows: ST = √(3² + 4²) = √(9 + 16) = √25 = 5 units. If, conversely, ST is known and one leg is missing, you would subtract the square of the known leg from the square of the hypotenuse and then take the square root to find the length of the missing leg.