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

Answer 1

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:

\[\tan (\theta) = \frac{ Fy }{ Fx }\]