# Question Video: The Resultant of Two Nonperpendicular Forces Mathematics

The angle between forces πΉβ and πΉβ is 112Β°, and the measure of the angle between their resultant and πΉβ is 56Β°. If the magnitude of πΉβ is 28 N, what is the magnitude of πΉβ?

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### Video Transcript

The angle between forces πΉ sub one and πΉ sub two is 112 degrees, and the measure of the angle between their resultant and πΉ sub two is 56 degrees. If the magnitude of πΉ sub one is 28 newtons, what is the magnitude of πΉ sub two?

Letβs begin by sketching the two forces with an angle of 112 degrees between them. We are also told in the question that the angle between the resultant force and πΉ sub two is 56 degrees. 112 minus 56 is equal to 56. Therefore, the angle between the resultant and πΉ sub one is also 56 degrees.

Using our knowledge of vector forces, we can create a parallelogram as shown. This can be split into two congruent triangles. Since πΉ sub one is equal to 28 newtons, we can use the sine rule to calculate πΉ sub two. The sine rule states that π over sin π΄ is equal to π over sin π΅, where the angles capital π΄ and capital π΅ are opposite the side lengths π and π.

Substituting in our values, we have 28 over the sin of 56 degrees is equal to πΉ sub two over the sin of 56 degrees. Multiplying through by the sin of 56 degrees, we get πΉ sub two is equal to 28. The magnitude of the force πΉ sub two is equal to 28 newtons.

We notice that this is the same value as πΉ sub one, which leads us to a general rule. If the resultant force bisects two forces, then the two forces will have the same magnitude. In this question, as the angle between the resultant force and πΉ sub one was 56 degrees and the angle between the resultant and πΉ sub two was also 56 degrees, then πΉ sub two and πΉ sub one must have the same magnitudes.