Homework Help: Four forces acting on a point

You can add them graphically head-to-tail too of course.

You need to pick two directions to be "positive" ... I'd pick "North" and "West" but some people will pick "East" to be positive since that looks like an x-axis.
This can simplify your working.

A 45deg triangle has sides 1-1-√2
A 60-30 triangle has sides 1-2-√3

so. sin(45)=cos(45)=1/√2
so. sin(60)= √3/2, cos(60)=1/2

For 4 and 5:
Once you have the total of the N-S and E-W components (and their directions) - draw them in on your graph.

From there you can draw in the resultant.
The resultant arrow will tell you how to get the direction.
To see what is expected - look at how the question describes the magnitude and direction of vectors that are not exactly on a N-S or E-W axis.

 

The graph you drew appears to be what was intended.
You have calculated the components of the resultant already - draw them on a similar graph. You are basically reversing the procedure you just used.

The stuff about triangles:
All trigonometry is based on right-angled triangles.
The angles used in the problem relate to a set of "special triangles" that have well-known and easily remembered properties. I brought it up because I wasn't sure you'd noticed.

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45-45-90 is what you get cutting a square in half corner-to-corner.
The ratio of it's sides are 1:1:√2 - the longest side is always the hypotenuse.

By definition: if the length of the hypotenuse is 1, then the length of the opposite side is the sine of the angle; if the adjacent side is 1, then the opposite side is the tangent of the angle and the hypotenuse is the secant. That is what those trig functions mean.

So:
tan(45)=1, and sec(45)=√2, can be read right off ...
sin(45)=1/√2 is obtained from similar triangles.
... no need for a calculator ;)

If you put two squares side-by-side to make an oblong, and cut the oblong corner-to-corner, you get a 30-60-90 triangle.
The ratio of the sides are 1-2-√3

Thus: tan(60)=√3 ... etc.

Whenever you see the angles 30, 45, or 60, you should think of these triangles. Also if you have a triangle where the two short sides are the same, or where one short side is half the hypotenuse.

Also learn 3-4-5 and 5-12-13.
3-4-5 triangles come up a lot!

http://www.onlinemathlearning.com/special-right-triangles.html