##### Need help in physics finding magnitude in word problem

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The 4.9 N weight is in equilibrium under the inﬂuence of the three forces acting on it. The F force acts from above on the left at an angle of α with the horizontal. The 5.9 N force acts from above on the right at an angle of 48◦ with the horizontal. The force 4.9 N acts straight down.

What is the magnitude of force F

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5.9 N ......... 4.9 N

...┌...... ......┐

.....\..... ...../

.....α\... .../ ß

-------- \ . /---------

...........◙

............|

............|

...........V 4.9 N

(It wasn't clear from your description whether the two angled forces act upward or downward, but if they're going to be in equilibrium with the weight, they should be upward.)

So,
we're in static equilibrium - the body is not accelerating. From the
vector version of F = ma, that means that the net vector force is zero.
If the vector force is zero, that means that orthogonal components of
the net vector force are zero. So, we take the horizontal and vertical
directions (which are orthogonal), find the net force components in
those directions, and set them equal to zero. We need to define the
positive and negative directions for those components, so let's say that
the positive x direction is to the right, and the positive y direction
is up.

In the x direction, the weight has no component. The 5.9 N force
component acts in the -x direction, with magnitude -5.9 N * cos α. The 4.9 N force component acts in the +x direction, with magnitude +4.9 *
cos ß. So, the sum of forces in the x direction (which is equal to
zero) is

ΣFx = -5.9 N * cos α + 4.9 N * cos ß = 0

In the y direction, the weight acts in the negative direction, with
magnitude -9.6 N. The other forces act in the +y direction, with
magnitude 5.5 N * sin α and 6.4 N * sin ß. So, the sum of forces in the
y direction (which is equal to zero) is

ΣFy = -4.9 N + 4.9 N * sin α + 4.9 N * sin ß = 0

So, we have 2 equations, and 2 unknowns, and we can solve. Let's start with the first equation.

-5.9 N * cos α + 4.9 N * cos ß = 0

5.9 * cos α = 4.9 * cos ß

cos α = (4.9 / 5.9) * cos ß

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