![]() Usually we are interested (as in the example above) in an angle other than the right angle. For a right triangle, the side opposite to the right angle is called the hypotenuse (from Greek for “stretching under”). Sides and angles that don’t touch are described as opposite. Sides and angles that touch are described as adjacent. Before we explain those functions, some additional terminology is needed. ![]() (It works the same in the metric system: 2.90 x 9.1 meters = 26.4 meters.) Sine, cosine and tangentĭepending on what is known about various side lengths and angles of a right triangle, there are two other trigonometric functions that may be more useful: the “ sine function” written as sin(x), and the “ cosine function” written as cos(x). Since the rigging point is 30 feet from the base of the mast, the mast must be 2.90 × 30 feet, or 87 feet tall. This means the slope of our rigging rope is 2.90. If we know how far the rope is rigged from the mast, and the slant at which the rope meets the deck, then all we need to determine the mast’s height is trigonometry. If the mast is perpendicular to the deck and top of the mast is rigged to the deck, then the mast, deck and rigging rope form a right triangle. Suppose you need to know the height of a sailboat mast, but are unable to climb it to measure. ![]() ![]() According to Victor Katz in “ A History of Mathematics (3rd Edition) (opens in new tab)” (Pearson, 2008), trigonometry developed primarily from the needs of Greek and Indian astronomers. Because early trigonometric works of Ancient Greece have been lost, it is not known whether Indian scholars developed trigonometry independently or after Greek influence. Though the field emerged in Greece during the third century B.C., some of the most important contributions (such as the sine function) came from India in the fifth century A.D. The word trigonometry is a 16th-century Latin derivative from the Greek words for triangle ( trigōnon) and measure ( metron).
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