\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Angle Measurements

The moon is huge, and the Sun even bigger still, yet they appear to have the same "size" in the sky. When you walk towards a friend, they appear to get "bigger". This apparent size can't be something measured in meters. In fact, it makes sense to think of it as an angle, measured in degrees or radians. The larger this angle is, the larger the object appears to be in our field of vision. We can use this idea to even talk about things that don't really have a real "size", such as the apparent distance of $90\deg$ from the horizon to the zenith (the point straight above our heads).