Answer
122 degrees
Work Step by Step
Looking at the picture provided, the watermelon seed lies at the point (-5,8), which is shown in black. Therefore, the position vector is the vector from (0,0) to the point (-5,8). The angle that this vector makes with the x axis (shown in red as $ \theta$) is the angle we are looking for.
To find this angle, we can use basic trigonometry.
We know that the length of the side opposite the angle is 8m (since y = 8m) and that the length of the side adjacent is 5m (since x = -5m).
We use the formula $ tan\theta = opposite/adjacent = 8/5$
Solving for $\theta$, we see that it equals 57.99 degrees.
However, the angle shown in the picture is the angle the vector makes with the NEGATIVE direction of the x axis, not the positive direction. In order to find the angle it makes with the positive, we need to find the complementary angle to $\theta$ (90-$\theta$ = 32). However, this will give us the angle from the vector to the positive y axis. In order to find the angle between the vector and the positive x axis, we need to add another 90 degrees (the separation between the x and y axis).
We then get that the angle = 90 + 32 = 122 degrees
