Question 1187582: A force of 100kg acting horizontally to the right is to be combined with one of 50 kg acting upward and to the right at an angle of 15 degrees with the vertical. Get the resultant force R and the angle between R and the 100kg force.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You can solve the problem using right triangles, or using an obtuse triangle and law of cosines. If the terms law of cosines and law of sines do not sound familiar, you probably were not taught that in math class, and should use right triangles.
You would decompose the 50 kg force into a vertical component and a horizontal component. The vertical component of the 50 kg force is the vertical component of the resultant force; and the horizontal component of R is the sum of the 100 kg horizontal force and the horizontal component of the 50 kg force.
SKETCH TO USE OBTUSE TRIANGLE:
SKETCH TO USE RIGHT TRIANGLES:
From the green triangle ABC you get the horizontal and vertical components of the 50kg force:
The red triangle APQ shows you  and its components.
The vertical component,  is
the vertical component of the 50kg force:
 .
The horizontal component,  is
the 100 kg force,  ,
plus the horizontal component of the 50kg force,
 .
We calculate the magnitude of the force  by applying Pythagoras theorem to red right triangle APQ:
We find the angle,  , between and the horizontal 100kg force from the trigonometric ratios of red triangle APQ.
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NOTES:
Check my calculations, because I make mistakes and my answers may have typos.
If you know how to solve obtuse triangles, you can use that way to solve the problem without my help.
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