Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
i need help figuring out how to do it, not just the answer please

Question

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
 i need help figuring out how to do it, not just the answer please

anonymous · Answer

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we can add the x and y components separately and use our knowledge of whether x and y are positive or negative in the quadrant in which it lies.

x components: 25*cos(10) - 30*cos(80) = Fx
y components: 25*sin(10) + 30*sin(80) = Fy

Magnitude [absolute value]:

$$F = \left| \sqrt{Fx^{2} + Fy^{2}} \right|$$

and the direction of F is the angle define by:

$$\tan (\theta) = \frac{ Fy }{ Fx }$$