Cosine and Sine rules to get magnitude and direction of a resultant force

In summary, to find the magnitude and direction of the resultant of a force of 11 kN at an angle of 50 degrees and a force of 6 kN at an angle of -30 degrees to the horizontal, you can use the cosine and sine rules. To find the magnitude, use the cosine rule and to find the direction, use the sine rule. Alternatively, you can resolve the forces into horizontal and vertical components and use geometry to find the resultant.
  • #1
baylayA
14
0
Use the cosine and sine rules to determine the magnitude and direction of the resultant of a force of 11 kN acting at an angle of 50 degrees to the horizontal and a force of 6 kN acting at an angle of -30 degrees to the horizontal.

helppp please
 
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  • #2
What have you tried doing? Have you drawn a diagram of the situation -- Will make things much easier.
 
  • #3
No i haven't.
Do you know how to find resultant forces with forces and angles from axises? because I have another problem like that and i have no idea how to do them
 
  • #4
Well maybe draw one then :smile: At least then you actually have a triangle to apply the cosine and sine rules to.

If you are given forces and angles relative to axes, you could again do the same thing and form a triangle to be solved with geometry, or perhaps easier would be to resolve each force into a horizontal and vertical component and add the components.
 
  • #5
Hi All
to get magnitude of resultant use cosin rule R^2= X^2+Y^2 – 2XYcosβ
to get the direction use sine rule = (Sin β /length of opposite line) = (sinθ/ length of opposite line)
 

What is the Cosine rule?

The cosine rule is a mathematical formula used to find the length of a side of a triangle when the lengths of the other two sides and the angle between them are known. It is also known as the Law of Cosines.

What is the Sine rule?

The sine rule is another mathematical formula used to find the length of a side of a triangle when the lengths of the other two sides and the angle opposite the unknown side are known. It is also known as the Law of Sines.

How do I use the Cosine rule to find the magnitude of a resultant force?

To use the Cosine rule to find the magnitude of a resultant force, you will need to know the magnitudes of the individual forces and the angle between them. You can then use the formula c² = a² + b² - 2ab cos(C), where c is the magnitude of the resultant force, a and b are the magnitudes of the individual forces, and C is the angle between them.

How do I use the Sine rule to find the direction of a resultant force?

To use the Sine rule to find the direction of a resultant force, you will need to know the magnitudes of the individual forces and the angle opposite the unknown direction. You can then use the formula sin(A)/a = sin(B)/b = sin(C)/c, where A, B, and C are the angles of the triangle and a, b, and c are the corresponding sides. The direction of the resultant force can then be found by solving for the unknown angle.

Can the Cosine and Sine rules be used for any triangle?

Yes, the Cosine and Sine rules can be used for any triangle, as long as you have enough information about the sides and angles. However, keep in mind that the Sine rule may have two solutions for the unknown angle in some cases, so you may need to use your knowledge of the triangle to determine which solution is relevant.

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