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a displace A has magnitude 25 m and another displacement B has magnitude 35 m. if the angle between the directions of ab is 60, then the magnitude of the resultant displacement is what?
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Use the cosine rule which is the generalized form of Pythagoras' theory/
C^2 = A^2 + B^2 - 2AB cos(theta)
-> C = sqrt( A^2 + B^2 - 2AB cos(theta) )
=sqrt( 25^2 + 35 ^ 2 - 2*25 * 35 * 1/2 )
= 31.2 m
Component of 35m. in same direction as A = (cos 60) x 35 = 17.5 metres.
Component perpendicular = (sin 60) x 35 = 30.31 metres.
Add 17.5 to 25m., = 42.5m.
Magnitude = sqrt. (42.5^2 + 30.31^2) = 52.2 metres.