Question 1202261
.
A construction crew wants to hoist a heavy beam so that it is standing up straight. They
tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end
A of the beam from the ground. When the beam makes an angle of 40o with the ground, the
top of the beam is 8 ft above the ground.
The construction site has some telephone wires crossing it.. The workers are concerned
that the beam may hit the wires. When the beam makes an angle of 60o with the ground,
the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to
standing up straight? Explain your answer
~~~~~~~~~~~~~~~~~~~~~~



        The analysis in the post by @mananth is incorrect

        (although the answer is right).


        I came to bring a correct solution.



<pre>
We find the length of the beam L from the condition

    sin(40°) = {{{8/L}}},  L = {{{8/sin(40^o)}}} = {{{8/0.64278760968}}} = 12.45 ft  (approximately).



The height of the wires is  L*sin(60°) + 2 = {{{12.45*(sqrt(3)/2)}}} + 2 = 10.78 + 2 = 12.78 ft.



The length of the beam, 12.45 ft, is less than the height of the wires, 12.78 ft,
which means that the beam will pass below the wires.             <<<---===  <U>ANSWER</U>
</pre>

Solved correctly.