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Calculating Side Lengths Using Tangent Functions in Right Triangles

This guide explains how to find the lengths of the sides in right triangles using the tangent function. When the side is opposite to the given angle, the formula is Opposite = tan(X) * Adjacent. Conversely, if the side is adjacent, the formula is Adjacent = Opposite / tan(X). For example, tan(490°) = 7, leading to the calculation of side lengths such as 6.09 or 6.7. Additionally, the relationships between angles like 220° and their respective sides are outlined with real-world examples.

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Calculating Side Lengths Using Tangent Functions in Right Triangles

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  1. 2.2 Finding Side Lengths Using Tan

  2. tan490 = 7 X X = 7 tan 490 X = 6.09 or 6 7 490 X

  3. tan220 = Y 10 tan220 (10) = Y 4.04 or 4 = Y Y 220 10

  4. If the side you are solving for is opposite the given angle, the formula is: Opp = tanX (Adj) If the side you are solving for is adjacent to the given angle, the formula is: Adj = Opp tanX

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