Answer:
261∠36° Newtons
Step-by-step explanation:
A straightforward way to find the resultant is to add the x- and y-components of the forces:
r = 300(cos(-30°), sin(-30°)) +180(cos(45°), sin(45°)) +250(cos(135°), sin(135°))
= (300√3/2 +180√2/2 -250√2/2, -300/2 +180√2/2 +250√2/2)
= (150√3 -35√2, -150 +215√2)
≈ (210.310, 154.056)
≈ 260.698∠36.22°
The resultant is approximately 261 Newtons at an angle of 36°.
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From components (x, y), the angle is found as arctan(y/x). The magnitude is found as √(x²+y²).
