SOLUTION: Two sides of a parallelogram measure 68cm and 83cm. Its smaller diagonal has a measure of 42cm. Find the largest interior angle of the parallelogram​.

Algebra ->  Polygons -> SOLUTION: Two sides of a parallelogram measure 68cm and 83cm. Its smaller diagonal has a measure of 42cm. Find the largest interior angle of the parallelogram​.      Log On


   

Question 1192097: Two sides of a parallelogram measure 68cm and 83cm. Its smaller diagonal has a measure of 42cm. Find the largest interior angle of the parallelogram​.
Answer by ikleyn(52803) About Me  (Show Source):
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Use the cosine law.


Find smaller interior angle "a" 


    42^2 = 68^2 + 83^2 - 2*68*83*cos(a)

    cos(a) = %2868%5E2%2B83%5E2-42%5E2%29%2F%282%2A68%2A83%29 = 0.863660524.

        a  = arccos(0.863660524) = 30.2698952  degrees.


Hence, the largest interior angle of the parallelogram is  180 - 30.2698952 = 149.73 degrees  (rounded).    ANSWER

Solved.