The resultant of two forces acting at right angles is 5 kgf and if they act at an angle of 60°, it is 37 kgf. The magnitudes of the forces are: A. 2 kgf, 3 kgf B. 3 kgf, 4 kgf C. 4 kgf, 5 kgf D. 5 kgf, 3 kgf

2 kgf, 3 kgf
3 kgf, 4 kgf
4 kgf, 5 kgf
5 kgf, 3 kgf

The correct answer is $\boxed{\text{B. 3 kgf, 4 kgf}}$.

Let $F_1$ and $F_2$ be the magnitudes of the two forces. We know that $F_1^2 + F_2^2 = 5^2 = 25$ and $(F_1 + F_2)^2 = 37^2 = 1369$. Solving these two equations, we get $F_1 = 3$ and $F_2 = 4$.

The two forces can be represented by two vectors, $F_1$ and $F_2$, that are at right angles to each other. The resultant force, $R$, is the diagonal of the rectangle formed by the two vectors. The magnitude of $R$ is given by the Pythagorean theorem:

$$R^2 = F_1^2 + F_2^2$$

In this case, $R = 5$, so $F_1^2 + F_2^2 = 25$.

If the two forces are at an angle of 60° to each other, the resultant force can be found using the law of cosines:

$$R^2 = F_1^2 + F_2^2 – 2F_1F_2\cos(60^\circ)$$

In this case, $R = 37$, so $F_1^2 + F_2^2 – 2F_1F_2\cos(60^\circ) = 1369$.

Solving this equation for $F_1$ and $F_2$, we get $F_1 = 3$ and $F_2 = 4$.

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