SOLUTION: I'm having difficulties solving this problem. Could someone please help me? Two forces with magnitudes of 131 and 52 newtons act on point with a resultant force of 100 newtons

Question 980796: I'm having difficulties solving this problem. Could someone please help me?
Two forces with magnitudes of 131 and 52 newtons act on point with a resultant force of 100
newtons. Find the angle, in radians, between the forces.
Enter answer accurate to four decimal places.
Thank you.
Found 2 solutions by Timnewman, KMST:
Answer by Timnewman(323) (Show Source): You can put this solution on YOUR website!
From your cosine rule,recall that
CosB=(c�+a�-b�)/2ac
Draw the vector and apply the formula.
from your diagramme,(i.e triangle) formed by the two vectors,
if a=52,
b=100
C=131
B=?
then,
cosB=(131�+52�-100�)/2*131*52
evaluating the above,
cosB=(9865)/(13624)
cosB=0.7241
B=cos-1(0.7241)
B=43.6068degres
now convert 43.6068� to radian
B=(pi/180)*46.6068
B=0.7612radian
the angle between them is 0.7612rad
HOPE THIS HELPS?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
While I was busy drawing pretty pictures, Tim was posting a more succinct answer.
I am posting my answer too, hoping that my drawings, and my different angle (pun intended) help too.
I am assuming that you have to find the angle ,
but we can also find the other angle in the parallelogram,
which is supplementary to : .
The resultant divides that parallelogram into two (congruent) triangles.
We need to apply to one of those triangles the law of cosines,
which is sort-of like an extension of the Pythagorean theorem,
for triangles that are not necessarily right triangles.
For law of cosines says .
Applying law of cosines to the triangle above, with , we get
and form that we get
(rounded)
Since they are supplementary angles (rounded) .
Inverse cosine function tells us that the angles, in radians are
and
RELATED QUESTIONS
I'm having a difficult time solving this problem. Could someone please help me? Two... (answered by solver91311)
I'm having trouble with the following example problem and would appreciate if I could get (answered by ikleyn,math_tutor2020)
I'm having trouble with the following example problem and would appreciate if I could get (answered by ikleyn,MathLover1)
Could you please help me with this problem? I am just starting in Trig and having some... (answered by dabanfield)
Need some help solving this word problem! -- Forces with magnitudes of 250 lbs and 130... (answered by Fombitz)
I am having difficulties rounding 60�15'18" down to just degrees and minutes. Please... (answered by solver91311)
Would you please help me solve this problem {{{6 - x/3 + 1 > 2/3}}} I'm having... (answered by jojo14344)
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10� and 100� (answered by Alan3354,KMST)
I really need help with solving this problem. Could someone please help me? 12 � x > 15... (answered by rfer)