What displacement must be added?

Question

What displacement must be added to a 50 cm displacement in the +X direction to give a resultant displacement of 85cm at 25 degrees?

Answer 1

so you want to subtract b = 85 ∠25º from a = 50 ∠0º

bx = 85 cos 25 = 77.0

by = 85 sin 25 = 35.9

ax = 50

ay = 0

rx = 77 - 50 = 27

ry = 35.9 - 0 = 35.9

r = √(27² + 35.9²) = 44.92

∠r = arctan 35.9/27 = 53º

.