Answer:
Nearly 84°
Step-by-step explanation:
In the attached diagram
- vector AB is vector u with magnitude 5 units
- vector AC is vector v with magnitude 7 units
- angle FAB = 30°
- angle FAC = 120°
So, angle BAC = 120° - 30° = 90°
A parallelogram ABCD is a rectangle, its diagonal vector AD is the sum of vectors AB and AC.
Consider right triangle ABD. In this triangle
[tex]\tan \angle BAD=\dfrac{BD}{AB}=\dfrac{AC}{AB}=\dfrac{7}{5}\\ \\\angle BAD\approx 54^{\circ}[/tex]
So, the sum vector AD has direction 30° + 54° = 84°
