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Math Help - Word problems ( I dont know how to start)

  1. #1
    Junior Member
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    Word problems ( I dont know how to start)

    Hi again... I'm having trouble with acouple of works problems. I just don't know where to start at.

    You are driving along the highway and see a sign indicating that you are about to enter a downhill slope of 10%. You realize that you are going to travel downward at an angle of _______ degrees to the horizontal. (Enter your answer as a mathematical expression or with at least two digits beyond the decimal point.)

    and

    You are about to land your Cessna airplane in Las Vegas. You are approaching the runway at a ground speed of 76 miles per hour and you are sinking at 230 feet per minute. (The ground speed is the speed of the point on the ground directly underneath your plane. You can also think of it as the horizontal component of your current velocity.) You are going to hit the runway at an angle of _______ degrees. (Enter your answer as a mathematical expression, or with at least three digits beyond the decimal point.)

    and

    You just took off in your trusty Lockheed SR-71. It's a fine windless day. Your instruments indicate a true air speed (speed relative to the surrounding air) of 400 miles per hour and a climb rate (vertical speed) of 10,000 feet per minute. You figure that your flight path makes an angle of _______ degrees with the horizontal. (Enter a mathematical expression or a decimal approximation with at least one digit beyond the decimal point.)
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  2. #2
    MHF Contributor
    Joined
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    Your three problems here involve right triangles.

    For the 1st one,
    hypotenuse = unknown
    vertical leg = 10
    horizontal leg = 100
    You are to find the angle opposite the 10-leg.

    tan(theta) = 10/100 = 0.1
    theta = arctan(0.1)
    theta = 5.71 degrees -----answer.

    --------
    For the 2nd one,
    hypotenuse = unknown
    vertical leg = 230 ft/min
    horizontal leg = 76 mi/hr
    You are to find the angle opposite the 230 ft/min -leg.

    First, make sure that the units of measurements must be the same. So convert the 76 mi/hr into ft/min (or the 320 ft/min into mi/hr.)
    There are 5280 ft per 1 mile, and 60 min per 1 hour, so,
    (230ft/min)*(1mi/5280ft)*(60min/1hr) = (230*1*60)/(5280*1) = 2.613636 mi/hr.
    Then, tan(theta) = 2.613636 / 76 = 0.03439
    theta = arctan(0.03439)
    theta = 1.9696 degrees. --------answer.

    ----------
    For the 3rd one,
    hypotenuse = 400 mi/hr
    vertical leg = 10,000 ft/min
    horizontal leg = unknown
    You are to find the angle opposite the 10,000 ft/min leg.

    Same units again,
    (10,000ft/min)*(1mi/5280ft)*(60min/1hr) = (10,000*1*60)/(5280*1) = 113.63636 mi/hr.
    Then, sin(theta) = 113.63636 / 400 = 0.28409
    theta = arcsin(0.03439)
    theta = 16.5 degrees. --------answer.
    Last edited by ticbol; October 9th 2005 at 05:06 AM.
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  3. #3
    Junior Member
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    Oh.... Okay Thank you for the help ticbol
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