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Math Help - inclination angle problem

  1. #1
    Junior Member
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    inclination angle problem

    A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 21 degrees and 23 degrees.
    How high (in feet) is the ballon?

    I have no clue how to solve for this without knowing any sides. Also need to know the formula to use and how to use it.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by badandy328 View Post
    A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 21 degrees and 23 degrees.
    How high (in feet) is the ballon?

    I have no clue how to solve for this without knowing any sides. Also need to know the formula to use and how to use it.
    The easiest way to do this is by using the tangent function. Let h be the height of the balloon (in feet) off the ground and d be the distance from the first milepost in feet. Then: \tan{23}\cdot{d} = h and \tan{21}\cdot{(d+5280)} = h. So you have two expressions which are both equal to h. You can equate them to solve for d and then use your value for d to find h.
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