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Math Help - 3D Trig

  1. #1
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    Exclamation 3D Trig

    From point C, an observer on a yacht measures the angle of elevation of point D at the top of a cliff to be 25 degrees. At this point the bearing of the cliff from the yacht is 300 degrees. After the yacht has sailed 100 m on a fixed course to pt A, the cliff is due north of the observer and the angle of elevation to the top of the cliff is 15 degrees. Point B is vertically below D at the base of the cliff.
    a) Show that angle ABC = 60 degrees.
    b) Show that BC = BDtan65 and that AB = BDtan75
    c) Calculatethe height of the cliff.
    I've done parts a + b. Could someone show me how to do c). The answer is 31 m but I can't seem to get it. I used Pythagoras' Theorem.
    Last edited by xwrathbringerx; April 16th 2010 at 06:51 PM.
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    From point C, an observer on a yacht measures the angle of elevation of point D at the top of a cliff to be 25 degrees. At this point the bearing of the cliff from the yacht is 300 degrees. After the yacht has sailed 100 m on a fixed course to pt A, the cliff is due north of the observer and the angle of elevation to the top of the cliff is 15 degrees. Point B is vertically below D at the base of the cliff.
    a) Show that angle ABC = 60 degrees.
    b) Show that BC = BDtan65 and that AB = BDtan75
    c) Calculatethe height of the cliff.
    I've done parts a + b. Could someone show me how to do c). The answer is 31 m but I can't seem to get it. I used Pythagoras' Theorem.
    Triangle ABC is not a right angled triangle so Pytrhogaras' theorem doesn't apply. Try the cosine rule (you should end up with a quadratic equation with BD as your variable.)
    Last edited by Debsta; April 16th 2010 at 07:37 PM.
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  3. #3
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    Quote Originally Posted by xwrathbringerx View Post
    From point C, an observer on a yacht measures the angle of elevation of point D at the top of a cliff to be 25 degrees. At this point the bearing of the cliff from the yacht is 300 degrees. After the yacht has sailed 100 m on a fixed course to pt A, the cliff is due north of the observer and the angle of elevation to the top of the cliff is 15 degrees. Point B is vertically below D at the base of the cliff.
    a) Show that angle ABC = 60 degrees.
    b) Show that BC = BDtan65 and that AB = BDtan75
    c) Calculatethe height of the cliff.
    I've done parts a + b. Could someone show me how to do c). The answer is 31 m but I can't seem to get it. I used Pythagoras' Theorem.
    hi

    since triangle ABC has its sides and one of its angle known , we can use the cosine rule with the help the answers obtained in (a) and (b)

    100^2=(BD\tan 75)^2+(BD\tan 65)^2-2(BD\tan 75)(BD\tan 65)\cos 60

    solving that , BD=31 m and it doesn't agree with the answer provided .
    Last edited by mathaddict; April 17th 2010 at 10:07 PM.
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  4. #4
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    Quote Originally Posted by mathaddict View Post
    hi

    since triangle ABC has its sides and one of its angle known , we can use the cosine rule with the help the answers obtained in (a) and (b)

    100^2=(BD\tan 75)^2+(BD\tan 65)^2-2(BD\tan 75)(BD\tan 65)\cos 60

    solving that , BD=53.3 m and it doesn't agree with the answer provided .
    Yes it does give the answer approx 31m as provided. Mathaddict - I think something went wrong with your calculations.
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  5. #5
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    Hmmm I keep on getting mathaddict's answer tooooo
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  6. #6
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    Quote Originally Posted by xwrathbringerx View Post
    Hmmm I keep on getting mathaddict's answer tooooo
    I'm not sure what you both are doing but I just did it again and got 31.
    It comes down to:
    10000 = 10.5237 x BD^2
    Did you get 10.5237 when you add the coefficients?
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  7. #7
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    Quote Originally Posted by Debsta View Post
    I'm not sure what you both are doing but I just did it again and got 31.
    It comes down to:
    10000 = 10.5237 x BD^2
    Did you get 10.5237 when you add the coefficients?
    Debsta is right . Sorry for creating this confusion .

    xwrathbringerx , try arranging your parantheses properly , then you should get 31 from the equation i posted earlier.
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