Final answer:
Using the Pythagorean theorem, we determine the length of the other leg of a right triangle with one leg of 3 units and a hypotenuse of 11 units to be approximately 10.58 units.
Step-by-step explanation:
To find the length of the other leg of a right triangle when given one leg and the hypotenuse, we use the Pythagorean theorem. For a right triangle with legs a and b, and hypotenuse c, the theorem states that a² + b² = c². Here, one leg (a) is 3 units, and the hypotenuse (c) is 11 units. To find the missing leg (b), we solve for b using the equation:
Write down the formula: a² + b² = c².
Insert the known values: 3² + b² = 11².
Simplify and solve for b: 9 + b² = 121.
Subtract 9 from both sides: b² = 112.
Take the square root of both sides: b = √112.
Find the square root to get the length of leg b: b ≈ 10.58 units.
Therefore, the length of the other leg of the right triangle is approximately 10.58 units.