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Math Help - grade 11 trig - Fire tower, Fire and evacuation time...

  1. #1
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    Unhappy grade 11 trig - Fire tower, Fire and evacuation time...

    Hi,

    I am a math tutor and one of my grade 11 students had this problem the other night. I am stumped and have sought help within my tutoring peers....we feel that there is some information missing.

    My student has a test tomorrow and her teacher is absent so I am hoping someone can confirm my assumption or point out what I am missing

    2 Fire towers are located 100K apart on high hills. The bearing from T to R is North east. A fire F is observed from tower T at N10degE and from tower R at N75degW. The town of Pretty Valley, at point V, is on a bearing of N25E from T and S70W from R. The observers report the wind is blowing the fire directly toward Pretty Valley at a rate of 8kmh. How many hours do the officials have to evacuate the town?

    I know I need to find the distance from F to V. However I cannot see how to get there. My colleague and I are both Bsc Math and we are stumped. I am just hoping it isn't us...maybe they left something out in the text!

    TIA,
    Tangled Curls
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  2. #2
    Bar0n janvdl's Avatar
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    Could you please draw me a picture? From above.
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  3. #3
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    picture

    I don't have software but here is a scan of my hand drawing.

    Thank you,
    Tangled curls
    Attached Thumbnails Attached Thumbnails grade 11 trig - Fire tower, Fire and evacuation time...-gr-11-fire-tower.jpg  
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  4. #4
    Bar0n janvdl's Avatar
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    Almost finished
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  5. #5
    Bar0n janvdl's Avatar
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    Look at it so far...
    Attached Thumbnails Attached Thumbnails grade 11 trig - Fire tower, Fire and evacuation time...-gr-11-fire-tower-2.jpg  
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  6. #6
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    I got to that point as well. We also figured that <VTR + <VRT = 45.

    .....
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  7. #7
    Bar0n janvdl's Avatar
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    Quote Originally Posted by tangledcurls View Post
    I got to that point as well. We also figured that <VTR + <VRT = 45.

    .....
    Angle V in TVR= 135 degrees...
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  8. #8
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    You mean angle (<) TVR, right
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  9. #9
    Bar0n janvdl's Avatar
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    Check this...
    Attached Thumbnails Attached Thumbnails grade 11 trig - Fire tower, Fire and evacuation time...-gr-11-fire-tower-3.jpg  
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tangledcurls View Post
    I don't have software but here is a scan of my hand drawing.

    Thank you,
    Tangled curls
    This is just a quick solution, i never thought really hard about this so there may be a more efficient way (maybe janvdl will come up with it), i never considered any right-triangles in my solution.

    Check my computation, i'm known for making silly mistakes, also, i used 2 decimal places for everything, so if you want a more accurate answer, redo the steps with more decimals

    see the modified diagram below


    By the law of sines:

    \frac {FR}{sin(35)} = \frac {TR}{sin(85)}

    \Rightarrow FR = \frac {100}{sin(85)} \cdot sin(35) = 57.58




    Also by the law of sines:

    \frac {VR}{sin(20)} = \frac {TR}{sin(135)}

    \Rightarrow VR = \frac {100}{sin(135)} \cdot sin(20) = 48.37




    Finally, by the law of cosines:

    FV^2 = FR^2 + VR^2 - 2 \cdot FR \cdot VR \cdot cos(35)

    \Rightarrow FV^2 = 57.58^2 + 48.37^2 - 2(57.58)(48.37)cos(35)

    \Rightarrow FV^2 = 1092.20

    \Rightarrow FV = 33.05

    And i think you can take it from here
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  11. #11
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by janvdl View Post
    Check this...

    Looks good so far to me
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  12. #12
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    how did you find the values for angles :

    <ftr = 35

    <vrt = 25?

    otherwise, I am good.

    Tks
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  13. #13
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    AAWWWW! BE nice to the 40 + age group....our brains slow down, LOL!

    I have to go get my kids from school and I will check back in when I get back....

    Thanks for you efforts

    TC
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  14. #14
    Bar0n janvdl's Avatar
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    Nice one Jhevon. I forgot my grade 10 trig... Thanks for helping out.
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  15. #15
    Bar0n janvdl's Avatar
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    Me a genius? Dont be silly. Im flattered though.

    No, your method is by far the most efficient. Although those right triangles and a little bit of trig could still solve this problem...
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