Geometry

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 of the beam from the ground. When
the beam makes an angle of 40 degrees with the
ground, the top of the beam is 8 ft above
the ground.
Th e construction site has some telephone
wires crossing it. Th e workers are
concerned that the beam may hit the wires.
When the beam makes an angle of 60 degrees 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?
Can I please get help with how to specifically solve this? I am very confused and I need step by step guidance.

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  1. As the problem is stated, of course they will because as it rises the horizontal distance from the pivot point at the ground decreases. If the wires are exactly above the tip of the bean at 60 deg, then they will be closer to the pivot point at more than 60deg
    Therefore I assume you have left out the horizontal overlap at 60 degrees and you need to figure out haw far back the beam moves as it pivots up those last two feet

    at 8 feet up
    sin 40 = 8/length of beam
    so L = 12.45 ft length

    then at 60 degrees
    sin 60 = h/12.45
    h = 10.78 high
    and horizontal distance is
    12.45 cos 60 = 6.23

    now at h = 2+10.78 = 12.78
    BUT that is higher than the beam is long :)
    No way it will hit the wires.

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  2. I think the answer is 12.78. But I'm not 100% honest.

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