The study of triangles and the trigonometric functions. One common use for trigonometry is to measure heights and distances that are awkward or impossible to measure by ordinary means. Surveyors use it to find heights of mountains and distances across lakes and countries; engineers use it in the design of large structures and roads; astronomers use it in accurate measurements of the time and in locating the position of objects in the sky; and navigators on the sea and in the air use it to find latitudes, longitudes, and direction. Trigonometry has evolved from use by surveyors, engineers, and navigators to applications involving ocean tides, the rise and fall of food supplies in certain ecologies, brain-wave patterns, the analysis of alternating-current electricity, and many other phenomena of a vibratory character.