Geometry & Trigonometry at the 700-800 Level

This is the largest hard-tier bank on the test, and it splits cleanly into two halves: right-triangle trigonometry and coordinate geometry.

Six archetypes cover nearly all of it. The two-observation height problem (a surveyor walks $d$ closer and re-sights) is solved by subtracting COTANGENTS: $h = \frac{d}{\cot\theta_{far} - \cot\theta_{near}}$. A hands you a triangle's shape, not its size — recognize the triple, then scale. scale lengths by and areas by , and part-to-part ratios must be converted to part-to-whole. : one triangle, three bases, three altitudes. , including running the midpoint backwards as . from a point to a line, which is never the vertical or horizontal gap.