Heights & Distances Cheat Sheet

Complete guide to Heights and Distances for competitive exams: basic trigonometric ratios (sin, cos, tan, cot, sec, cosec) for angles 0°, 30°, 45°, 60°, 90°, angle of elevation (line of sight above horizontal), angle of depression (line of sight below horizontal), height of a tower or building using angle of elevation and distance, distance from a point using angle of elevation and height, finding height when two angles of elevation are given (from different points or at different times), problems on shadows and sun altitude, problems on height of cloud or balloon, problems involving multiple objects (two towers, poles, buildings), problems on moving towards or away from object, problems using trigonometric identities, approximation using Pythagoras theorem, and shortcut tricks for SSC, Banking, Railway, UPSC, and other government exams.