Final answer:
The length of the missing leg of a right triangle with a hypotenuse of 11cm and another leg of 7cm is approximately 8.49 cm, calculated using the Pythagorean theorem.
Step-by-step explanation:
To find the length of the missing leg of a right triangle when the hypotenuse and one leg are known, we can use the Pythagorean theorem, which 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). The formula is a² + b² = c².
In this case, the hypotenuse (c) is 11 cm and one leg (a) is 7 cm. We are looking for the length of the other leg (b).
Step-by-step, the calculation is:
- Write down the Pythagorean theorem: a² + b² = c².
- Substitute the values for a and c into the equation: 7² + b² = 11².
- Calculate the squares: 49 + b² = 121.
- Rearrange the equation to solve for b²: b² = 121 - 49.
- Subtract: b² = 72.
- Take the square root of both sides: b = √72.
- Calculate the final answer: b = 8.49 cm (rounded to two decimal places).
The length of the missing leg, b, is approximately 8.49 cm.