The measures of the angles between the resultant and two applied forces are 65 degrees and 42 degrees. If the magnitude of the resultant is 24 pounds, find to the nearest pound the magnitude of the smaller force.

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- March 17th 2009, 02:52 PMblame_canada100force vectors
The measures of the angles between the resultant and two applied forces are 65 degrees and 42 degrees. If the magnitude of the resultant is 24 pounds, find to the nearest pound the magnitude of the smaller force.

- March 17th 2009, 03:47 PMskeeter
sketch a parallelogram with one angle = 107 degrees

the diagonal that connects the opposite congruent 107 degree angles is the resultant 24 lb force ... the sides of the parallelogram are the two summed force vectors.

work out the values of other angles using your parallel postulates from geometry, then use the law of sines to solve for the side lengths - March 17th 2009, 04:56 PMSoroban
Hello, blame_canada100!

I found a solution.

But there may be (there*should*be) a more elegant one.

Quote:

The measures of the angles between the resultant

. . and two applied forces are 65° and 42°.

If the magnitude of the resultant is 24 pounds,

. . find to the nearest pound the magnitude of the smaller force.

Code:`R S`

* *

|* * |*

| * * | *

| * b 24 * | *

| * * | *

| * * | *

| * 65° * | *

| * * 42° | *

* - - - * - - - - - - - * - - - *

P a Q

The two vectors are: .

. . .The resultant is: .

We have: .

Hence: .

Solve the system for and and see which is smaller.