Resultant

**gracey** · December 14th 2008, 02:15 AM

Two forces magnitude 5N and 7N act on a body. The angle between the forces is 55 degrees. The resultant has magnitude R and acts at an anlge to Ѳ to the 5N force , as shown in the diagram. Calculate R and Ѳ.

thanks

**running-gag** · December 14th 2008, 03:38 AM

Hi

$R \cos\theta = 5 + 7 \cos(55)$
$R \sin\theta = 7 \sin(55)$

$R^2 = (R \cos\theta)^2 + (R \sin\theta)^2 = (5 + 7 \cos(55))^2 + (7 \sin(55))^2 = 74 + 70 \cos(55)$
$R = \sqrt{74 + 70 \cos(55)} = 10.68 N$

$\sin\theta = \frac{7 \sin(55)}{\sqrt{74 + 70 \cos(55)}}$

$\theta = 32.4\, deg$

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