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Right Triangle Research Paper

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There are six trigonometric ratios that one must know in order to find any angle in a right triangle. There are various of ways to remember these trigonometric ratios, but the most common way is through SOHCAOTOA. By having this clear in your memory, it will allow one to remember at least the three basic trigonometric ratios: Sine (sin.), Cosine (cos.), and Tangent (tan.). Before one learns about how SOHCAOTOA is split up, we must learn about the angles in a right triangle. First off, the hypotenuse is the longest line in a triangle, then in order to find the adjacent and opposite, one must locate where the angle. Upon locating the angle, we can conclude that the opposite is further away from the angle, whereas the adjacent is the closer one …show more content…

In short, these three trig. ratios are the reciprocal of sine (sin.), cosine (cos.), and tangent (tan.). Although many may assume that cosecant is the reciprocal of cosine, it is actually that of sine, which means that cosecant is hypotenuse over opposite. Thereafter, that leaves us with secant, which is in fact the reciprocal of cosine, demonstrating that it is hypotenuse over adjacent. Nonetheless, cotangent is the last trig. ratio, meaning that it is the reciprocal of tangent, being rather adjacent over opposite. Now, we know the formulas for these trigonometric functions being: Csc=HypotenuseOpposite, Sec=HypotenuseAdjacent, and Cot=AdjacentOpposite . For example, the triangle on the next page is a 7-24-25 right triangle, and we must determine the six trigonometric ratios for angle C of the right triangle. Based off this information, we can determine that the adjacent is 7, with the opposite being 24 and hypotenuse as 25. In order to find the sine of angle C, we must write out Sin C =OppositeHypotenuse and plug in the numbers to equal Sin C=2425. Next, in order to find the cosine of angle C, by writing out Cos C=AdjacentHypotenuse and plugging in the adjacent and hypotenuse number to equal Cos C=725. After solving for the sine and cosine of the right triangle, we must find the tangent being Tan C=OppositeAdjacent.

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