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
Hi
$\displaystyle R \cos\theta = 5 + 7 \cos(55)$
$\displaystyle R \sin\theta = 7 \sin(55)$
$\displaystyle R^2 = (R \cos\theta)^2 + (R \sin\theta)^2 = (5 + 7 \cos(55))^2 + (7 \sin(55))^2 = 74 + 70 \cos(55)$
$\displaystyle R = \sqrt{74 + 70 \cos(55)} = 10.68 N$
$\displaystyle \sin\theta = \frac{7 \sin(55)}{\sqrt{74 + 70 \cos(55)}}$
$\displaystyle \theta = 32.4\, deg$