Final answer:
The angle between two forces of equal magnitude required for the resultant force to also have an equal magnitude to the individual forces is 90 degrees, as per the Pythagorean theorem applied to right-angled vectors.
Step-by-step explanation:
The question is asking what angle between two forces of equal magnitude would result in a resultant force that is also of equal magnitude to the two original forces. According to the principles of vector addition, when two equal magnitude vectors are placed at a right angle to one another, we can use the Pythagorean theorem to calculate that resultant force. Therefore, for the resultant to be equal in magnitude to the individual forces, the angle between them must be 90 degrees (°). This is because according to the Pythagorean theorem, the resultant vector (hypotenuse of the triangle) equals the magnitude of one of the legs when the triangle is isosceles right-angled, that is when the angles are 90 and 45 degrees.
This relates to Newton's third law, which implies that forces of equal magnitude and opposite direction cancel each other, but that is not the case here since we are looking for a non-zero resultant force.