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# What is an application of trigonometry?

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One application of trigonometry in the real world is determining the distance and location of faraway objects. This is useful in navigation and in surveying. Historically, trigonometry was also applied to determine the position of heavenly bodies, but this use has been supplanted by linear algebra in modern times.

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Using trigonometry, it is possible to measure objects, no matter how large or inaccessible they are. Knowing the distance and angle between the observer and an object, the height of a tall object such as a cliff can be ascertained. The height is treated as one side of a triangle, while the distance between the observer and the top of the cliff is treated as another side of the same triangle. The problem of finding the height of a tall object is turned into a simple trigonometric calculation. The same method can be applied to objects lying along the plane of the Earth, such as a distant lake. This method is called triangulation and has a long history of application in navigation and map-making.

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## Related Questions

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The ancient Greeks were the first to develop the conceptual framework of trigonometry. The noted Greek astronomers Hipparchus, Menelaus and Ptolomy contributed in advancing the field.

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Trigonometry is used in many fields of applied and practical sciences, such as astronomy, geography, physics and engineering. Trigonometry is used in astronomy to determine the distance from Earth to various nearby stars by observing the parallax shift with Earth's orbit around the Sun as a baseline.

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In the real world, sinusoidal functions can be used to describe mechanical functions such as the swinging of a pendulum or natural phenomena such as hours of daylight. Sinusoidal functions graph wave forms.

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Trigonometry has applications in a number of scientific fields, ranging from geography and astronomy to engineering and physics. One of the most important early real-life examples of trigonometry involved using the knowledge that the earth was a sphere for navigation. Ptolemy put trigonometry to work in his work "Geography", and Christopher Columbus used trigonometry in finding his way from Spain to what he thought was India but ended up being the New World.