Finding x and y Components of Vector Sum

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McAfee
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Homework Statement



Text problem: The two vectors a and b in Fig. 3-28 have equal magnitudes of 12.6 m and the angles are θ1 = 35° and θ2 = 108°. Find (a) the x component and (b) the y component of their vector sum r, (c) the magnitude of r, and (d) the angle r makes with the positive direction of the x axis.


Vector diagram with x and y axes meeting at origin O; vector a from O at angle theta 1 above the x-axis, and vector b from the tip of a at angle theta 2 measured from a dashed extension of a's line.



The Attempt at a Solution


I wanted to make sure I use the right angle for vector B.
Handwritten work: vectors A = 12.6 cos 35° i + 12.6 sin 35° j and B = 12.6 cos 143° i + 12.6 sin 143° j, then x-component sum 0.259 m, y-component sum 14.8 m, magnitude sqrt(0.259² + 14.8²) = 14.8 m, and angle arctan(14.8/0.259) = 88.9974° ≈ 89.0°.

Also just wanted to check my work.
 
I didn't check your actual calculations, but your method looks fine.