Chapter 12: Applications of Trigonometry

Applications of Trigonometry puts the previous chapter's ratios to work on real height-and-distance problems, using the angle of elevation (looking up) and angle of depression (looking down) — first with problems needing one triangle, then two. A 45° elevation angle always means the height equals the horizontal distance, since tan45°=1 exactly.

Drawing the triangle incorrectly from the word description — particularly mixing up elevation and depression — is the most common mistake, and it happens before any trigonometry is even applied. This is the practical payoff of the entire Trigonometry chapter: translating a scenario into a correctly labelled triangle is a genuinely different skill from the ratio calculations themselves.