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Math Help - Trig class - bearing problem

  1. #1
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    Trig class - bearing problem

    Please, help me to solve the problem:
    Two fire towers are located 85 km apart on hills A and B. The bearing from A to B is north east. A fire F is observed from tower A at N10E and from B at N75W. The town at point C is on bearing of N25E from A and S70W from B. The observers report the wind is blowing the fire directly toward C at a rate 9km/h. How many hours do the officials have to evacuate the town?

    I can't find the distance FC
    Thank you.
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  2. #2
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    Quote Originally Posted by Romanka View Post
    Please, help me to solve the problem:
    Two fire towers are located 85 km apart on hills A and B. The bearing from A to B is north east. A fire F is observed from tower A at N10E and from B at N75W. The town at point C is on bearing of N25E from A and S70W from B. The observers report the wind is blowing the fire directly toward C at a rate 9km/h. How many hours do the officials have to evacuate the town?

    I can't find the distance FC
    Thank you.
    I've attached a sketch.

    1. Calculate all side lengthes of the triangle ABF (marked red)

    2. Calculate all side lengthes in triangle ABC (marked blue)

    3. Calculate the side length FC in triangle ACF.

    For your confirmation I've added an approximate result.
    Attached Thumbnails Attached Thumbnails Trig class - bearing problem-fire_town.png  
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  3. #3
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    I don't understand how to get angels in ABC . I know how to find <C=135, but what about <A and <B?
    And THANK YOU!!!
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  4. #4
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    Quote Originally Posted by Romanka View Post
    I don't understand how to get angels in ABC . I know how to find <C=135, but what about <A and <B?
    And THANK YOU!!!
    Complete my sketch by adding the given angles. Then you can calculate the interior angles in the two triangles in question.
    Attached Thumbnails Attached Thumbnails Trig class - bearing problem-fire_town.png  
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  5. #5
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    Sorry, I'm completely stupid , but
    how to get the angles <A =20 and <B=25? It can be easily proved that their sum is 45 degrees... Why aren't they 22 and 23 degrees, or 18 and 27, for example?
    If I could catch about angles then I can find everything for the problem.
    Thank you!
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  6. #6
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    Quote Originally Posted by Romanka View Post
    Sorry, I'm completely stupid , but
    how to get the angles <A =20 and <B=25? It can be easily proved that their sum is 45 degrees... Why aren't they 22 and 23 degrees, or 18 and 27, for example?
    If I could catch about angles then I can find everything for the problem.
    Thank you!
    According to your question the line AB and the North direction include an angle of 45 = NE.

    According to your question the line AC and the North direction include an angle of 25.

    Therefore the angle at A is 45 - 25 = 20

    You'll get the interior angle at B in a similar way:

    The line BC and South include an angle of 70.
    The line BA and South include anangle of 45.

    Therefore the \angle(CBA) = 70^\circ - 45^\circ = 25^\circ

    etc + andsoon
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  7. #7
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    Quote Originally Posted by earboth View Post
    According to your question the line AB and the North direction include an angle of 45 = NE.

    According to your question the line AC and the North direction include an angle of 25.

    etc + andsoon
    that's exactly what I missed!
    Thank you so much!
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