A radio mast stands at the origin of a site plan, with its top at the point A(0, 0, 12)…

Step 1. The direction ratios. $(3 - 0, 4 - 0, 0 - 12) = (3, 4, -12)$.

Step 2. The length. $AB = \sqrt{9 + 16 + 144} = 13$ metres.

Step 3. The direction cosines. From the top to the anchor they are $l = \dfrac{3}{13} \approx 0.231$, $m = \dfrac{4}{13} \approx 0.308$ and $n = -\dfrac{12}{13} \approx -0.923$.

Step 4. The angle with the mast. The angle with the upward $z$-axis is $\cos^{-1}(-0.923) \approx 157.38^\circ$. The wire is a line, so the acute angle is $180^\circ - 157.38^\circ = 22.62^\circ$.