Math

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?

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  1. we see that the length of the beam is

    8/sin40 = 12.45 ft

    At 60 degrees, the top is

    12.45sin60 = 10.78 ft high

    So, the wire is 12.78 ft up.

    Since the beam is only 12.45 ft long, it will not touch the wires.

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