SOLUTION: An overhead crane is suspended from a ceiling by two chains. One chain is 4.6 m long and forms an angle of 60^\circ with the ceiling. The other chain is 6.4 m long. What angle does

Algebra ->  Trigonometry-basics -> SOLUTION: An overhead crane is suspended from a ceiling by two chains. One chain is 4.6 m long and forms an angle of 60^\circ with the ceiling. The other chain is 6.4 m long. What angle does      Log On


   

Question 1168194: An overhead crane is suspended from a ceiling by two chains. One chain is 4.6 m long and forms an angle of 60^\circ with the ceiling. The other chain is 6.4 m long. What angle does the larger chain make with the ceiling?
Answer by ikleyn(52818) About Me  (Show Source):
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An overhead crane is suspended from a ceiling by two chains. One chain is 4.6 m long
and forms an angle of 60° with the ceiling. The other chain is 6.4 m long.
What angle does the larger chain make with the ceiling?
~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let 'a' be the angle which the larger chain makes with the ceiling.

Angle 'a' is opposite to the 4.6 m side;  angle 60° is opposite to the 6.4 m side.


Use the sine law

    sin%2860%5Eo%29%2F6.4 = sin%28a%29%2F4.6.


From this equality

    sin(a) = sin%2860%5Eo%29%2A%284.6%2F6.4%29 = %28sqrt%283%29%2F2%29%2A%284.6%2F6.4%29 = 0.622455759.


Therefore, angle 'a' is

    'a' = arcsin(0.622455759) = 38.4956896 degrees.


ANSWER.  Angle 'a' is approximately 38.5°.


CHECK.  We see that the greater angle (60°) is opposite to the longer side (6.4 m), 

         which is consistent with Geometry.

Solved.