Posted by Hanson on .
Okay I posted this before but I am still not sure. How would you solve for M?
The resultant of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20° and 52°. Find the magnitude of the larger force.

Precalculus 
Damon,
a and b are forces
components in direction of resultant > resultant
a cos 20 + b cos 52 = 80
components perpendicular to resultant sum to zero
a sin 20 = b sin 52
2 linear equations, two unknowns, solve 
Precalculus 
Reiny,
make a sketch to get ∆ABC where ∢B = 20° and ∢A = 52°
AB is one vector, and AC is your second vector with BC the resultant.
so ∢C = 108°
By the sine law
AB/sin108 = 80/sin52
AB = 80sin108/sin52 = 96.55 or 97 pounds. 
Precalculus 
Damon,
Question #2
Which of us is a physicist and which is a mathematician ? :) 
Precalculus 
Hanson,
Damon, how would I solve that's what I am confused on
Reiny, That answer does not fit with any of the given answers 
Precalculus 
Reiny,
Ok, let's do that triangle again.
draw AB the first vector, and AC, the second vector.
draw AP, the resultant.
angle BAP = 52
angle CAP = 20
AP = 80
complete the parallelogra BACP, then
angle APB=20
angle B = angle C = 108
AC/sin52 = 80/sin108
AC = 80sin52/sin108 = 66.3
(should not have jumped to a triangle too soon) 
Precalculus 
Kate,
Thanks reiny! But one question how do you know when to use the triangle method and when to use parallelogram?

Precalculus 
Reiny,
A good hint is to always draw the parallelogram first with the resultant being the diagonal.
That way you can use alternate angles (that is where I messed up)
The diagonal (resultant) will then give you the triangles.
Depending on the information given, you would then use either the sine law or the cosine law.