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15 September, 22:21

A 12.0-cm segment makes a 108.0-degree angle with a 16.0-cm segment. To the nearest tenth of a cm, find the third side of the triangle determined by this SAS information.

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  1. 15 September, 22:34
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    Begin by using the cosine rule to find the unknown side.

    Where a - unknown side, b is 12, c is 16 and angle in between is 108°

    The cosine rule ...

    a² = b² + c² - 2bc cosA

    = 12² + 16² - (2*12*16 cos108°)

    = 518.655076

    Taking the positive square root ...

    a = 22.774

    a = 22.8 cm nearest tenth
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