Two forces acting in opposite direction have resultant `10 N` and when acting perpendicularly have resultant `50 N`. Find the magnitude of forces.

Explanation

To solve the problem, we need to find the magnitudes of two forces \( A \) and \( B \) given the following conditions:

1. When the forces act in opposite directions, the resultant is \( 10 \, \text{N} \).
2. When the forces act perpendicularly, the resultant is \( 50 \, \text{N} \).

Let's denote the magnitudes of the two forces as \( A \) and \( B \).

### Step 1: Analyze the first condition (forces in opposite directions)
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