A force of 240 Newtons acts at 30 degrees. Another force of 500 Newton acts at the same point at 240 degrees. Find the resultant vector and its magnitude and angle. I got the magnitude using the pythagorean theorem. Now I don't know the degree.
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Have you found the $x$-component and the $y$-component of the resultant? – Toby Mak Oct 03 '19 at 22:33
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3@TobyMak is right. You need to find the x and y components of the resulting vector and then you need to take the arctangent of this ratio to get the angle. – Ryan Oct 03 '19 at 22:35
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The resulting vector will bisect angle between the forces. So... – Vasili Oct 03 '19 at 22:40
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@Vasya Bisect, really? How so? – Ted Shifrin Oct 04 '19 at 00:17
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Find new vector:
$240cos(30)+500cos(240)=-42.1539$
$240sin(30)+500cos(240)=-313.0127$
Now use $tan$ to find the degree. $arctan\frac{-313.0127}{-42.1539}$$=82$
So the angle is $82$ so $180+82=262$ since it lies in the third quadrant
Sina Babaei Zadeh
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The thing I don't understand is, the third quadrant means the angle measure is between 180 and 270. How do I know if I subtract 82 from 270 OR if I add it to 180? – Dylan Oct 04 '19 at 01:17
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Its because when you calculated $tanx$ to find the degree, you assumed $x$ was adjacent and $y$ was opposite leg of the triangle. So you have to use the $x$-axis not the $y$ axis as a reference – Sina Babaei Zadeh Oct 04 '19 at 02:37