How to Calculate Angle From Tangents

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Trigonometry uses sine, cosine and tangent to represent the ratio of two sides of a right triangle to one of the angles. The tangent function represents the ratio of the opposite side divided by the adjacent side. To find the angle measurement, you need to use the inverse tangent, or arctangent function on the calculator. This function is often abbreviated tan^-1. If you know or can measure the opposite and adjacent sides of the triangle, you can compute the unknown angle.

    Measure the side length of the right triangle. For example, you might have a right triangle with the side lengths 6, 8 and 10. The longest side of the triangle will be the hypotenuse, the other two sides are known as the legs.

    Identify the adjacent side of the triangle to the angle. This will be the side that helps for the angle that is not the hypotenuse. For example, if the angle you want to find is formed by the 6-inch side and the 10-inch side, the adjacent side would be 6 inches.

    Identify the opposite side of the triangle relative to the angle. The opposite side of the triangle will be the leg that does not help form the angle. In this example, if the angle you want to find is formed by the 6-inch side and the 10-inch side, the opposite side would be the 8-inch side.

    Divide the opposite side by the adjacent side. In this example, you would divide 8 by 6 and get about 1.333.

    Use your calculator to find the inverse tangent of the result from Step 4 to calculate the angle measurement. On many calculators, you can use the inverse tangent function by hitting "2nd" and then "TAN." Finishing this example, the inverse tangent of 1.333 equals about 53.13, meaning the unknown angle is 53.13 degrees.

    Things You'll Need

    • Scientific calculator
    • Measuring tape (optional)


About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."

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