Short physics question involving angle and magnitudes

Question

What is the value of an angle between two forces of equal magnitudes, when the resultant force's magnitude is the same? The answer is 120 degrees but I don't know how to approach this question

Answer 1

Thank you for this is juicy question, For the the three forces including the resultant to have equal magnitudes they must form a triangle with three equal sides and three equal angles between them and this is the description of an equilateral triangle with three equal forces and three equal angles of 60 degrees. So in principle the angle formed between the two forces is 60 degrees, but also if you complete the parallelogram you will find out the angle formed between the forces can also be 120 degrees if the first force F direction is east and the 2nd force F direction is North-West. The resultant force F direction is North-East