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The angle between two forces of equal magnitude is 60 degrees and the magnitude of their resultant is 71 root three newtons.
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What is the magnitude of the forces?
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When two forces 𝐹 one and 𝐹 two are acting on a point with resultant 𝑅, where 𝐹 one makes an angle 𝜃 one with 𝑅 and 𝐹 two makes an angle 𝜃 two with 𝑅, we can apply the formula 𝐹 one divided by sin 𝜃 two is equal to 𝐹 two divided by sin 𝜃 one, which is equal to 𝑅 divided by sin 𝜃 one plus 𝜃 two.
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As the two forces are of equal magnitude, we know that 𝐹 one is equal to 𝐹 two.
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As these forces are equal, we can also say that the angle between 𝐹 one and 𝑅 and the angle between 𝐹 two and 𝑅 are also equal: 𝜃 one equals 𝜃 two.
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As the angle between the two forces was 60 degrees, we can see that the angle between 𝐹 and 𝑅 is 30 degrees.
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This gives us the equation 𝐹 divided by sin 30 is equal to 71 root three divided by sin 60.
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Rearranging this equation gives the force 𝐹 is equal to 71 root three divided by sin 60 multiplied by sin 30.
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This is equal to 71 newtons.
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Therefore, the magnitude of the forces is 71 newtons.