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a traingle has an area 48 square cm and its shorter sides have lengths 9cm and 12cm. find the lagest angle of the traingle.

  • MATH -

    Area of triangle = side1*side2*sin(angle between them)/2

    so 48 = 1/2(12)(9)sin ß
    sin ß = 48/54
    ß = 62.7º or 117.26º

    If the angle is 62.7
    Using the cosine law I found the side across from the 62.7º to be 11.226 and then using the sine law once more found the angle across from the side of 9 to be 45.44º surely making all three angles acute.

    So the largest angle in the triangle must be in the second case, where the angle was 117.7º

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