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Math Help - Bearings Problem Using the Sine Rule

  1. #1
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    Bearings Problem Using the Sine Rule

    Hello! Any help with the following problem is much appreciated. I am enjoying the topic of trigonometry, but I seem to be having a little trouble with bearings. Thank you in advance.

    A river has parallel banks which run directly east-west. Kylie takes a bearing to a tree on the opposite side. The bearing is 047*T. She then walks 10 m due east, and takes a second bearing to the tree. This is 305*T. Find:

    a. her distance from the second measuring point to the tree.
    b. the width of the river, to the nearest metre.


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  2. #2
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    Quote Originally Posted by JadeKiara View Post
    Hello! Any help with the following problem is much appreciated. I am enjoying the topic of trigonometry, but I seem to be having a little trouble with bearings. Thank you in advance.

    A river has parallel banks which run directly east-west. Kylie takes a bearing to a tree on the opposite side. The bearing is 047*T. She then walks 10 m due east, and takes a second bearing to the tree. This is 305*T. Find:

    a. her distance from the second measuring point to the tree.
    b. the width of the river, to the nearest metre.
    What is the unit of 047*T and 305*T? What is T?
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  3. #3
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    In this case, T stands for true, as it is a true bearing.

    The * sign means degrees.
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    Quote Originally Posted by JadeKiara View Post
    In this case, T stands for true, as it is a true bearing.

    The * sign means degrees.
    Whether 305 degrees correct bearing for 10 m displacement? Or any typo?
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  5. #5
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    Perhaps, if you cannot understand true bearings, than attempt it with normal bearings:

    A river has parallel banks which run directly east-west. Kylie takes a bearing to a tree on the opposite side. The bearing is N93*
    E. She then walks 10 m due east, and takes a second bearing to the tree. This is N55*W. Find:

    a. her distance from the second measuring point to the tree.
    b. the width of the river, to the nearest metre.
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    Quote Originally Posted by JadeKiara View Post
    Perhaps, if you cannot understand true bearings, than attempt it with normal bearings:

    A river has parallel banks which run directly east-west. Kylie takes a bearing to a tree on the opposite side. The bearing is N93*
    E. She then walks 10 m due east, and takes a second bearing to the tree. This is N55*W. Find:

    a. her distance from the second measuring point to the tree.
    b. the width of the river, to the nearest metre.
    Let A and B are the initial and the final positions of Kylie. P is the position of tree. Let PD perpendicular to AB.
    The
    tan(92) = PD/AD
    tan(35) = PD/BD. BD = 10 - AD. Solve these equations and find PD and PB.
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  7. #7
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    Hello JadeKiara
    Quote Originally Posted by JadeKiara View Post
    Hello! Any help with the following problem is much appreciated. I am enjoying the topic of trigonometry, but I seem to be having a little trouble with bearings. Thank you in advance.

    A river has parallel banks which run directly east-west. Kylie takes a bearing to a tree on the opposite side. The bearing is 047*T. She then walks 10 m due east, and takes a second bearing to the tree. This is 305*T. Find:

    a. her distance from the second measuring point to the tree.
    b. the width of the river, to the nearest metre.


    Based on your original post, the diagram looks like the one I've attached.

    Then, using the Sine Rule:
    \frac{BP}{\sin43^o} = \frac{10}{\sin\angle APB}
    Can you complete it now?

    Grandad
    Attached Thumbnails Attached Thumbnails Bearings Problem Using the Sine Rule-untitled.jpg  
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  8. #8
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    Oh, I cannot thank you enough, Grandad. I must say, I have been frustrated to tears over this problem for hours - and your help has cleared everything up. I shall forge ahead with more problems like this now, for practice!

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