Answer:
54.0°
Step-by-step explanation:
We have that:
u=<cos 30°, 4sin30°>
This implies that:
u=<½√3, 2>
Also, v=<3cos 45°, 3sin 45°>
v=<3√2/2, 3√2/2>
u+v=<2.99,4.12)
The direction of u+v, is the angle, it makes with the positive x-axis.
This is given by;
[tex] \theta = { \tan}^{ - 1} ( \frac{y}{x} )[/tex]
[tex] \theta = { \tan}^{ - 1} ( \frac{4.12}{2.99} )[/tex]
[tex] \theta = 54.03[/tex]
To the nearest tenth, the direction is 54.0°
