Final answer:
The question requires the use of Pythagoras' theorem to find the ratio x/y, where x and y are sides of a right triangle. An exact value cannot be given without specific lengths. Dimensional analysis ensures accurate unit conversions in related calculations.
Step-by-step explanation:
The question is asking to use Pythagoras' theorem to work out the exact value of a ratio x/y, where x and y are lengths of sides of a right-angled triangle. To use Pythagoras' theorem, you would need to identify the lengths of the two shorter sides (perpendicular to each other) and the hypotenuse, which is the longest side opposite the right angle. If x and y represent lengths of the shorter sides, then the theorem tells us that the square of the hypotenuse (z) is equal to the sum of the squares of the other two sides (x^2 + y^2).
For example, if we were given the lengths of x and y, Pythagoras' theorem would allow us to calculate z. However, without specific numbers for x and y, we can't provide an exact numerical value for x/y. If x is the hypotenuse and y is one of the other sides, then using Pythagoras' theorem would allow you to find the length of the third side. Once all three sides are known, the ratio x/y can be calculated.
Unit conversions, such as from inches to centimeters, are also relevant to accurately solve problems when different measurements are provided in differing units. Using dimensional analysis and unit conversion factors can ensure that the calculations are made correctly.