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26 May, 08:54

Los angeles is 1,744 miles from chicago; chicago is 714 miles from new york; and new york is 2,451 miles from los angeles. The tree cities form a triangle. Find the measure of the angle in the triangle whose vertex represents chicago.



121°



170°

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  1. 26 May, 09:16
    0
    170°

    Step-by-step explanation:

    Let a be the distance from Los Angeles to Chicago = 1744 miles, b be the distance from Chicago to New York = 714 miles and c be the distance from New York to Los Angeles = 2451 miles.

    A is the angle opposite to side a, B is the angle opposite to side b and C is the angle opposite to side c.

    Therefore the angle at Chicago is C.

    From cosine rule:

    c² = a² + b² - 2ab * cos (C)

    2ab * cos (C) = a² + b² - c²

    cos (C) = (a² + b² - c²) / 2ab

    Substituting:

    cos (C) = (1744² + 714² - 2451²) / 2*1744*741

    cos (C) = - 0.986

    C = cos⁻¹ ( - 0.986) = 170°
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