## anonymous one year ago Really need help, Will FAN and MEDAL A forest ranger at an observation point A sights a fire in the direction N27degrees10'E. another ranger at an obseraion point B, 6.0 miles due east of A, sights the same fire at N52degrees40'W. Approx. the distance from each other the observation points to the fire. I drew a picture but I want to see someone else interpretation of the information

1. anonymous

@Michele_Laino if you're not busy can you help me again. I don't remember if I asked you this one

2. Michele_Laino

N27degrees10'E means that I'm heading towards North, right?

3. anonymous

Yes, you're in the North and heading East

4. Michele_Laino

ok!

5. Michele_Laino

like this? |dw:1432759303858:dw|

6. anonymous

Yes I have that part

7. Michele_Laino

so the complete drawing is: |dw:1432759443568:dw|

8. Michele_Laino

sorry: |dw:1432759585590:dw|

9. Michele_Laino

is my drawing right?

10. anonymous

I think so

11. Michele_Laino

12. Michele_Laino

am I right?

13. Michele_Laino

|dw:1432759935107:dw|

14. anonymous

yeah, i think so

15. Michele_Laino

Now, we can apply the law of sines, so we can write: $\Large \frac{6}{{\sin \left( {89^\circ 50'} \right)}} = \frac{{AC}}{{\sin \left( {37^\circ 20'} \right)}}$

16. Michele_Laino

so: $\Large AC = \frac{{6 \times \sin \left( {37^\circ 20'} \right)}}{{\sin \left( {89^\circ 50'} \right)}} = ...?$

17. Michele_Laino

what is AC?

18. anonymous

=3.6

19. Michele_Laino

hint: we can write this: 37° 20'= 37.33 degrees 89°50'=89.83 degrees

20. Michele_Laino

I got AC=3.638 miles

21. Michele_Laino

22. Michele_Laino

Now, similarly, using the law of sines again, we can write: $\Large \frac{6}{{\sin \left( {89^\circ 50'} \right)}} = \frac{{BC}}{{\sin \left( {62^\circ 50'} \right)}}$

23. Michele_Laino

so we get: $\Large BC = \frac{{6 \times \sin \left( {62^\circ 50'} \right)}}{{\sin \left( {89^\circ 50'} \right)}} = ...?$ So, what is BC?

24. Michele_Laino

hint: 62° 50'=62.83 degrees 89° 50'=89.83 degrees

25. anonymous

5.3

26. Michele_Laino

that's right! I got 5.338 miles