# What does it mean that a line forms an obtuse angle with a coordinate axis? Aren't all angles either acute or right?

I'm self-studying from Vector Analysis and Cartesian Tensors by Kendall because my lecturer is somewhat lacking, and I got conceptually stuck on excersise 1.11 dealing with direction cosines. What does it mean when we say that a line makes an obtuse angle with an axis? Is there a norm on which direction you're supposed to be looking from?

Also, a cosine squared appears in here (which gives 4 candidate solutions), but even if I reject two because it's obtuse or acute, that still leaves me with two potential answers and the solutions only say 135 degrees.

"Inclined at an obtuse angle to the $z$-axis" now means that the ray you're looking has its infinite end below the $xy$-plane, where the $z$-coordinates are negative.
This gives you only one solution for the angle -- in space geometry it doesn't make sense to count angles with sign; all angles measures are expected to be between $0$ and $180^\circ$.
The omitted word is "positive." It should say "to the positive $z$-axis." Likewise, "$x$-axis" and "$y$-axis" should (respectively) be replaced by "positive $x$-axis" and "positive $y$-axis\$."