Explorable · Trigonometry · 2026
Drop a Perpendicular
An interactive explainer for solving triangles. Every textbook case, from three sides to the ambiguous side-side-angle, comes down to one move: draw a perpendicular, solve the two right triangles it makes, and use their shared height to connect them. The cosine and sine rules fall out as shortcuts.
- Steps through all five cases on one persistent triangle, or on real problems: a frame, two boats, a building, a roof and a cable.
- Derives the cosine and sine rules from the construction, and shows why side-side-angle can have two answers.