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Math Help - cosine equation

  1. #1
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    Jul 2008
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    cosine equation

    5.) The model

    .342Dcos(theta) + h cos^2(theta)=16D^2/Vo^2

    is used to construct accidents in which a vehicle vaults into the air after hitting an obstruction. Vo is velocity in feet per second of the vechicle when it hits, D is distance (in feet) from the obstruction to the landing point, and h is the difference in height (in feet) between landing point and takeoff point. Angle theta is the takeoff angle, the angle between the horizontal and the path of the vehicle. Find theta to the nearest degree if Vo=60, D=80, h=2.


    my work:

    =.342(80)cos(theta)+(2)cos^2(theta)=16(80)^2/(60)^2

    =27.36cos(theta)+2cos^2(theta)=455.1111111

    now I used the quadratic formula to try to solve but i got:

    cos(theta)=(approx.)8.25
    cos(theta)=(approx.)-21.93

    so can i graph it?can i factoring?what is the next step?
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  2. #2
    Member
    Joined
    May 2008
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    106
    the RHS of your equation is wrong

    \frac{16(80)^2}{60^2}=\frac{256}{9}=28.44444...

    you must have made a mistake because remember (for real \theta)

    -1 \leq \cos \theta \leq 1
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