Question

A force vector has a magnitude of 720 N and a direction of 38 degree north of east. Determine the magnitude and direction of the components of the force that point along the north-south line and along east-west line.

Answer 1

443.3 N

567.4 N

Step-by-step explanation:

Consider the triangle ABC

AC = hypotenuse = magnitude of force vector = F = 720 N

AB = adjacent = Component of force along east-west line =
`F_(x)`

BC = Opposite = Component of force along north-south line =
`F_(y)`

θ = Angle = 38 deg

In triangle ABC

`Sin38 = (BC)/(AC)`

`Sin38 = (F_(y))/(F)`

`0.616 = (F_(y))/(720)`

`F_(y)` = 443.3 N

Also, In triangle ABC

`Cos38 = (AB)/(AC)`

`Cos38 = (F_(x))/(F)`

`0.788 = (F_(x))/(720)`

`F_(x)` = 567.4 N