Assuming the angle made by a vector refers to the angle it makes with the positive horizontal axis, take the dot product of <em>u</em> with the vector (1, 0), and recall that
<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>)
where <em>θ</em> is the angle made by the vectors <em>a</em> and <em>b</em>. Then
<em>u</em> • (1, 0) = ||<em>u</em>|| ||(1, 0)|| cos(<em>θ</em>)
We have
<em>u</em> • (1, 0) = 5×1 + 8×0 = 5
||<em>u</em>|| = √(5² + 8²) = √89
||(1, 0)|| = √(1² + 0²) = √1 = 1
so that
5 = √89 cos(<em>θ</em>)
cos(<em>θ</em>) = 5 / √89
<em>θ</em> = arccos(5 / √89) ≈ 57.99°
