Help badly needed understanding this problem. Determining length and direction of vectors

[DWelsh]

I'm taking an engineering intro class, and this problem has me stuck:

 

"Vector R in Fig. 4.9 is the difference between vectors T and S. If S is inclined at 28 degrees from the vertical and the angle between S and T is 32 degrees, calculate the magnitude and direction of vector R. The magnitude of S and T are 19 cm and 36 cm, respectively. " Fig. 4.9 Is simply three lines pointing diagonally downward from the top right, with R being horizotal, T below R, and S below T (sorry, I cant find a picture to upload). I only have pre-calc under my belt (no physics) but I feel like this shouldn't be to hard to understand. I'm just finding it impossible to figure out HOW to solve this. I have access to the answer:(R = 18.8 cms, direction is horizontal) but I really need to know how to do it. Any help is greatly appreciated. Thanks

[zztop]

Tr

 

I'm taking an engineering intro class, and this problem has me stuck:

 

"Vector R in Fig. 4.9 is the difference between vectors T and S. If S is inclined at 28 degrees from the vertical and the angle between S and T is 32 degrees, calculate the magnitude and direction of vector R. The magnitude of S and T are 19 cm and 36 cm, respectively. " Fig. 4.9 Is simply three lines pointing diagonally downward from the top right, with R being horizotal, T below R, and S below T (sorry, I cant find a picture to upload). I only have pre-calc under my belt (no physics) but I feel like this shouldn't be to hard to understand. I'm just finding it impossible to figure out HOW to solve this. I have access to the answer:(R = 18.8 cms, direction is horizontal) but I really need to know how to do it. Any help is greatly appreciated. Thanks

Triangle cosine rule teaches us that:

 

[latex]R^2=S^2+T^2-2S*T*cos x[/latex]

 

where x is the angle between S and T.

 

I'll let you figure why R is horizontal

Edited February 14, 2017 by zztop

[DWelsh]

Thank you for your help. I can see that this is just simple trigonometry now.