Final answer:
To find side lengths b and c in right triangles, use the Pythagorean theorem: a² + b² = c². Solve for the unknown side length, ensuring that all lengths are in the same unit, and round to the nearest tenth. Negative side length values are not feasible in this context.
Step-by-step explanation:
The subject of this question is Mathematics, and it is most relevant to a High School level education. The question pertains to finding the lengths of sides b and c in right triangles using the Pythagorean theorem, which is represented by the equation a² + b² = c². To find the length c, known as the hypotenuse, you would rearrange the formula to c = √(a² + b²). If instead you need to find the length of side b, you would rearrange the formula to b = √(c² - a²).
To apply this theorem, you first need to ensure all side lengths are in the same unit and then simply plug in the known side lengths and solve for the unknown side. You would round the result to the nearest tenth as required. Without specific values for side lengths a or c, we cannot calculate the exact lengths for b or c, but this process explains how to approach problems of this nature.
When dealing with directly provided constants such as a = 1.00, b = 10.0, and c = -200, it's important to recognize that these are likely related to a different context, possibly the coefficients of a quadratic equation. For the Pythagorean theorem, all side lengths must be positive, rendering a negative value for c nonsensical.