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A tunnel for a new highway is to be cut through a mountain that is 260 feet high. At a distance of 200 feet from the base of the mountain, the angle of elevation is 36 degrees. From a distance of 150 feet on the other side of the mountain, the angle of elevation is 47 degrees. Approximate the length of the tunnel to the nearest foot.

  • trig -

    I drew triangle ABC where BC is a horizontal (the road) and angle B is 36° , and is on the left side of the diagram.
    Angle C = 47° , on the right side
    D is on BC and is the altitude of the mountain of 260 feet
    I let BD = 200+x , and DC = 150+y

    in the left triangle,
    tan 36° = 260/(200+x)
    200+x = 260/tan 36
    x = 260/tan36 - 200 = 157.86 feet

    find y in the same way.....

    length of tunnel = x+y
    = ....

  • trig -

    y=92.5
    x=157.9
    x+y=250.4ft

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