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Chapter 3 - 3.47

47. Let A denote the magnitude of A ; similarly for the other vectors. The vector equation is A + B = C

where B =8 . 0mand C =2 A . We are also told that the angle (measured in the ‘standard’ sense) for

A is 0 ◦ and the angle for C is 90 ◦ , which makes this a right triangle (when drawn in a “head-to-tail”

fashion)where B isthesizeofthehypotenuse. UsingthePythagoreantheorem,

B = A 2 + C 2 =

⇒

8 . 0= A 2 +4 A 2

whichleadsto A =8 / √ 5=3 . 6m.