Find the resultant of the three vectors shown in figure .
.

Explanation

Take the axes as shown in the figure.
The x-component of the 5.0 m vector ` = 5.0 m cos37^0`
`=4.0m`
the x-component of the 3.0 m vector `= 3.0m`
and the x-component of the 2.0 m vector = ` 2.0 m cos90^0`
0.
Hence, the x-component of the resultant
` 4.0 m+3.0m+ 0 = 7.0 m`
They y-component o the 5.0 m vector = `5.0 m sin 37^0`
` =3.0m`
the y-component of the 3.0 m vector =0
and the y-component of the 2.0 m vector = 2.0 m.
3.0 m+0+2.0 m=5.0 m.
The magnitude of the resultant vector
=`sqrt((7.0m)^2+(5.0m)^2)`
`=8.6m`
If the angle made by the resultant with the X-axis is theta, then
` tan theta` = (y-component)/(x-component) = 5.0/7.0 or, `theta`= `35.5^@`.