Precalculus
posted by Hanson .
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.

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 
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. 
Question #2
Which of us is a physicist and which is a mathematician ? :) 
Damon, how would I solve that's what I am confused on
Reiny, That answer does not fit with any of the given answers 
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) 
Thanks reiny! But one question how do you know when to use the triangle method and when to use parallelogram?

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.