Help with Vector Components: Finding Magnitude and Direction

[godkills]

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What are the magnitude and direction of the total displacement for the treasure hunt illustrated in Figure 3-9? Assume each pace is .750 m in length.

Question found in Physics 4th edition James S. Walker.

My question is when finding the components of vector C how do you find the angles and use the cos and sin? Or do you use tan? I honesty was lost because there was no example in the book that covered this particular material. There is no angle that was given or anything like that how can I find the components of C? And also when finding the angle for Vector D i had some troubles such as which numbers do I use?

Components of A = A_x = 0 A_y = 3.75

Components of B = B_x = 2.25 B_y = 0

Please guide me through this I am honesty lost in what formulas do I use and where is the angles? D=

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[jhae2.718]

For the direction of C, what does southeast correspond to on a unit circle? (You can take the reference angle here...)

Then, what functions relate a distance and an angle to its components/projections?

After you find the angle for C and take the vector sum to get D, you can find the angle of D by relating its components. What trig function relates the x and y components of a triangle?

 

[godkills]

45 degrees so C_x = 2.12 C_y = -2.12

D = 4.66 m angle 20.5

pyth therom

 

[jhae2.718]

You also need to take into account what direction the vector points. C is points to the right and down, so what should the signs of the components of C be?