# Precalculus

posted by .

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 -

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 -

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 -

Question #2
Which of us is a physicist and which is a mathematician ? :)

• Precalculus -

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 -

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 -

Thanks reiny! But one question how do you know when to use the triangle method and when to use parallelogram?

• Precalculus -

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.

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