Question 1168194
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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?
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<pre>
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(60^o)/6.4}}} = {{{sin(a)/4.6}}}.


From this equality

    sin(a) = {{{sin(60^o)*(4.6/6.4)}}} = {{{(sqrt(3)/2)*(4.6/6.4)}}} = 0.622455759.


Therefore, angle 'a' is

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


<U>ANSWER</U>.  Angle 'a' is approximately 38.5°.


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

         which is consistent with Geometry. 
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Solved.