Football Pattern Vectors Question

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The discussion focuses on calculating the x and y components of a football player's displacement based on the lengths of three legs and the angle between two of them. Leg A measures 3.0 meters, leg B measures 13.0 meters, and leg C measures 23.0 meters, with an angle φ of 38.0° between legs B and C. The correct x component of displacement is calculated as (A+B+C)x = 31.336 meters, while the y component is incorrectly calculated as (A+B+C)y = -3.16 meters. The confusion arises from the use of trigonometric functions for the y component, particularly regarding the angle used for leg A.

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In a practice, a football players runs the pattern shown above. Leg A is 3.0 meters long, leg B is 13.0 meters long and leg C is 23.0 meters long. The angle φ between legs B and C is 38.0°. (Legs A and B are perpendicular.)

1.)What is x component of her displacement? (Assume the x direction to be horizontal on that drawing above.)
(A+B+C)x =
2.)What is y component of her displacement? (Assume the y direction to be vertical on that drawing above.)
(A+B+C)y =

For to find the x and y component I did the following:

Ax=3cos0°=3
Bx=13cos38°=10.24
Cx=23cos(-38°)=18.12

Ay=3sin90°=3
By=13sin38°=8.00
Cy=23sin(-38°)=-14.16


(A+B+C)x=31.336 which I got correct but for (A+B+C)y=-3.16 which I didn't get correct and I don't know what I did wrong??
 
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Welcome to PF.
I'm a bit confused how leg A and B are perpendicular but there is only a 38 deg angle difference between the two. For Ay you have 3sin90 but for Ax you have 3cos0?
Seems that your Ay is incorrect since you got part 1.
In the future illustrations go a long way.
 
Here is a picture.
 

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    football pattern.gif
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By = 0
 

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