# Q: Find the magnitude and direction of the resultant of two forces?Note: "This Question is About Mechanics(Math)

Expert:

To determine the modulus of the resultant R of two forces F1 and F2, we use the cosine theorem. Given that the angle ABC of the force triangle is 180°-α, we write the following expression based on the cosine theorem:

R² = F1² F2² - 2 * F1 * F2 * cos(180 - α)

since cos(180 - α) = -cos(α) , we get:

R = √(F1² F2² 2 * F1 * F2 * cos(α))

The formula R = √(F1² F2² 2 * F1 * F2 * cos(α)) calculates the modulus of the resultant of two forces whose lines of action form an arbitrary angle α between themselves.

To determine the direction of the resultant R with respect to the given forces, that is, to determine the angles β and γ between the line of action of the resultant and the lines of action of the given forces F1 and F2, we use the sine theorem:

F1/sin(y) = F2/sin(b) = R/sin(180 - α)

Given that sin(180 - α) = sin(α) , we get

sin(b) = (F2/R) * sin(α)

sin(y) = (F1/R) * sin(α)

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