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Math Help - Question on Trig Functions and Angles

  1. #1
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    Question on Trig Functions and Angles

    I'm having trouble figuring out what to do on these two questions.

    1. 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 don't under stand how to figure this one out without the distances of the base.


    2.For find the values of the trigonometric functions based on the given one.
    Note: The answer must be given as a fraction. NO DECIMALS.

    If then
    =



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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by badandy328 View Post
    I'm having trouble figuring out what to do on these two questions.

    1. 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 don't under stand how to figure this one out without the distances of the base.


    2.For find the values of the trigonometric functions based on the given one.
    Note: The answer must be given as a fraction. NO DECIMALS.

    If then
    =



    Uhm...well I am not sure but you might have copied this down wrong but arcse\bigg(\frac{7}{5}\bigg)=arcos\bigg(\frac{5}{7  }\bigg)

    Which does not have an exact value answer...so there would be decimals unless you are saying like csc\bigg(arcsec\bigg(\frac{7}{5}\bigg)\bigg)=\frac  {7\sqrt{6}}{12}?
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  3. #3
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    Quote Originally Posted by badandy328 View Post
    I'm having trouble figuring out what to do on these two questions.

    1. 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 don't under stand how to figure this one out without the distances of the base.


    2.For find the values of the trigonometric functions based on the given one.
    Note: The answer must be given as a fraction. NO DECIMALS.

    If then
    =



    For the first question, use tan(\alpha) = \frac{h}{d} and tan(\beta) = \frac{h}{d+5280}. Then you have:
    d tan(\alpha) = (d+5280) tan(\beta) and you can solve for d and then h.
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  4. #4
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    I don't know this tan a and b thing you are showing me for the first question.

    For the second question I copied it down right. I figured out that cos = 5/7. The rest i don't see how you find
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