Answer to Question #87326 in Analytic Geometry for Adri

Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

One can notice that the angle between the two acting forces is

$$120\degree - 30\degree = 90\degree$$

Hence, applying the parallelogram rule in the vector sum we obtain a rectangle with the diagonal being equal to the resultant force (see the figure).

According to Pythagorean theorem:

$$F = \sqrt{F_1^2 + F_2^2}=\sqrt{150^2 + 100^2} \approx 180.28 \, pounds$$

The orientation is

$$\phi = 30\degree + \alpha = 30\degree + \arctan{\frac{F_2}{F_1}} \approx 63.69 \, \degree$$

Answer: the resultant force is 180.28 pounds acting at 63.69 °