Calculating Resultant Force of Two Forces: 8N and 11N at 30 Degrees

[laura11]

two forces with a magnitude 8N and 11N act on a large object. The angle between the forces is 30 degrees. Calculate the magnitude of the resultant force.

the answer is 18.4 in the back of the book



I drew a diagram and made a triangle... i was trying to use the triangle rule
but like i don't know if the values are supposed to be the length of the sides? and if they are well.. i still don't know what to do haha
im just really lost in this question

 

[Mark44]

Draw a parallelogram with two of the adjacent sides being your two vectors, and the angle between them 30 degrees. The long diagonal of the parallelogram will be the magnitude of the resultant vector. Use basic trig to figure out the length of the diagonal.

 

[xcvxcvvc]

just pretend one vector is at a convenient angle and that the other is 30 degrees from it. then calculate the magnitude of their sum.

for example, if the 11 was at 90 degrees, you could then have the 8 be at 90 +/- 30 (you get the same magnitude at the end -- just keep using 60 or 120 throughout the entire calculation)

so you have
|11j +cos(60)*8 + sin(60)*8*j| or |11j +cos(120)*8 + sin(120)*8*j|

really, any arbitrary assignment of an angle to the first one will work. you just need to break the vectors into rectangular components, add, then take the root of the squares. So your first vector should either be purely real or purely imaginary so you only need to break 1 vector into component form. Otherwise, you'll need to break two.