Answer to Question #178937 in Analytic Geometry for John withers

Question

Two forces of magnitude 80𝑁 and 45𝑁 act on an object, with an angle between the forces of 100°. What is the resultant force?

Answer 1

Let force $F_1=80N$

Let the force $F_2=45N$

The resultant of the two forces can be obtained using:

$$R^2 = F_1^2+F_2^2-2F_1F_2\cos\theta\\$$

The angle formed between the two forces lies in the second quadrant. Thus the value of $\cos\theta$ will be negative.

Thus:

$$R^2 = 80^2 + 45^2 - 2\times80\times45\times\cos(180\degree-100\degree)\\ R^2 = 6400 + 2025 -7200 \times \cos80\degree\\ R^2 = 8425 - 7200 \times 0.1737\\ R^2 = 8425 -1,250.64\\ R^2 = 7,174.36\\ R = \sqrt{7,174.36}\\ R = 84.7N$$