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18 June, 09:00

There are two non congruent triangles where B=55 degrees a=15 and b=13. Find the measures of the angles of the triangle with the greater perimeter. Round to the nearest tenth if necessary.

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  1. 18 June, 09:02
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    The side c needs to be 12.85 for the triangle to have greatest perimeter

    Step-by-step explanation:

    We are given;

    b = 13

    a = 15

    Angle at b: B = 55°

    Let's find side c.

    Using the law of cosines, we have;

    b² = a² + c² - 2ac•cos (B)

    13² = 15² + c² - 2•15•c•cos (55)

    169 = 225 + c² - 30c•cos (55)

    c² - 30c•cos (55) + 225 - 169 = 0

    c² - 30c•cos (55) + 56 = 0

    c² - 30c• (0.5736) + 56 = 0

    c² - 30c• (0.5736) + 56 = 0

    c² - 17.208c + 56 = 0

    Using quadratic formula;

    c = [ - (-17.208) ± √ ((-17.208) ² - (4•1•56) ]/2 (1)

    c = [17.208 ± √ (296.115 - 224) ]/2

    c = 8.604 ± 4.246

    To have the greater perimeter, we need the larger value of c, thus we will use the positive sign and ignore the negative one;

    Thus,

    c = 8.604 + 4.246 = 12.85
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