# Thread: grade 11 trig - Fire tower, Fire and evacuation time...

1. ## 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

2. Could you please draw me a picture? From above.

3. ## picture

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

Thank you,
Tangled curls

4. Almost finished

5. Look at it so far...

6. I got to that point as well. We also figured that <VTR + <VRT = 45.

.....

7. Originally Posted by tangledcurls
I got to that point as well. We also figured that <VTR + <VRT = 45.

.....
Angle V in TVR= 135 degrees...

8. You mean angle (<) TVR, right

9. Check this...

10. Originally Posted by tangledcurls
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

11. Originally Posted by janvdl
Check this...

Looks good so far to me

12. how did you find the values for angles :

<ftr = 35

<vrt = 25?

otherwise, I am good.

Tks

13. 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

14. Nice one Jhevon. I forgot my grade 10 trig... Thanks for helping out.

15. 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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