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.
Respond to this Question
Similar Questions

physics
Two forces acting on a body in opposite directions,have the resultant velocities of 10newton. if they act at right angles to each other, the resultant is 50 newton.find the two forces. 
Precalculus
Okay I am soo confused with these two questions: 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. … 
PHYSICS
the sum of the magnitude of two forces acting at a point is 18 and the magnitude of their resultant is 12.if the resultant is at 90 degree with the force of the smaller magnitude, then their magnitudes are: 
mechanics
the greatest and the least resultant of twoforces acting on a particle are the 35KN and 5 KN respectively. if 25KN is the magnitude of the resultant for the given system of forces f1 and f2 .prove that the forces are acting at right … 
mathematics
the greatest and the least resultants of two forces acting on a body are 35kN and 5kN respectively,determine the magnitude of the forces,what would be the angle between these forces if the magnitude of the resultant is stated to be … 
precalculus
Forces with magnitudes of 250 pounds and 130 pounds, act on an object at angles 45°and 61° respectiviley , with the positive axis. Find the direction and magnitude of the resultant of these forces. 
science
The greatest and least resultant of two forces acting at a point is 29 kgwt and 5 kgwt respectively.If each force is increased by 3 kgwt.Find the resultant of the two new forces when acting at right angles to each other? 
science
The greatest and least resultant of two forces acting at a point is 29 kgwt and 5 kgwt respectively.If each force is increased by 3 kgwt.Find the resultant of the two new forces when acting at right angles to each other? 
Science
Two forces acting in the opposite direction have a resultant of 10N. If they act at the right angles to each other the resultant is 50N .the magnitude of the forces are 
physics
the sum of magnitudes of two forces acting at a point is 18n and the magnitude of their resultant is 12n. if the resultant makes an angle of 90 degree with the force of smaller magnitude,what are the magnitude of two forces