SOLUTION: the smallest angle of a triangle with sides 9cm, 11cm and 13 cm

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Question 1209423: the smallest angle of a triangle with sides 9cm, 11cm and 13 cm

Answer by ikleyn(52788) About Me  (Show Source):
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the smallest angle of a triangle with sides 9cm, 11cm and 13 cm
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In any triangle, the smallest angle is opposite to the shortest side.


In the given triangle, the smallest angle is opposite to the 9 cm side and is
concluded between the 11 cm and 13 cm sides.


Write the cosine law for the shortest side of 9 cm


    9^2 = 11^2 + 13^2 - 2*11*13*cos(a)


where "a" is the angle under the question.


From this equation,

    cos(a) = %2811%5E2+%2B+13%5E2+-+9%5E2%29%2F%282%2A11%2A13%29 = 209%2F286%29 = 19%2F26 = 0.730769231.


So, the angle "a" is


    a = arccos(0.730769231) = 43.04907978 degrees.    ANSWER


You may round it as you want.

Solved.