# Math Help - finding the magnitude using vector

1. ## finding the magnitude using vector

Hi
I need help on the following question:

The direction of force F1 is in a direction west of north with magnitude of 5 newton, and force F2 is unchanged ( which is northeast with a magnitude of 6 newton). If the resultant force F = F1 + F2 now points directly to the north, find the direction of F1 and the resulting F.

My problem is i cannot seem to get the magnitude but i can get the direction:

This is how i got the direction:

When i drew the vectors it was not a right angle triangle so i used this formula:

$\frac{sinA}{a} = \frac{sinB}{b}$

$sin\theta = \frac{6sin(45)}{5}$

$\theta = 58.05$degrees

This is my attempt of finding the magnitude:

using the formula: $c^2 = a^2 + b^2 - 2abcos(\theta)$

$F^2 = 5^2 + 6^2 - 2 * 5 * 6 * cos(58.05)$

$F = \sqrt{61 - 60cos(58.05)}$

F = 5.41N however book's answer says its 6.89N

P.S

2. In your solution θ is the angle between F2 and north.
To find the resultant of F1 and F2 ,. you must know the angle between F1 and F2.
In the above problem, what is the angle between F1 and F2?

3. Hi

First of all its better to write the exact question since I cant really understand your question the same thing goes with your solution

However the followings steps might help you if you have ideas of component
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Step-1 : Take the component of F2 along east-west direction

Step-2 : The east west component of F1 should be opposite to the same of F2 hence (why? because their resultant has only north south value)

Now to get the value of resultant F

Step 3: Take the north south component of both F1 and F2 and add them its magnitude of your resultant

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Tip: Try not to use sine rule here something doesn't smell right in your answer..check the included angles you are using..