Mimi_x3 4 years ago Cindy is some distance NW from a building Don is some distance due North of a building. If Don is twice as far as Cindy from the building and they are 40m apart, calculate their distances to the building to the nearest one-tenth of metre. Can someone please explain step by step on how to do this, I'm like so lost

1. xactxx

Okay. |dw:1316163703925:dw|

2. Mimi_x3

Do i calculate x by soh cah toa thing ?

3. xactxx

no, the triangle is not guaranteed to be right angled.

4. xactxx

do you know of the sine rule?

5. Mimi_x3

Yup, do i use the sine rule ?

6. MeEngr

use law of cosines or law of sines here to find the angles from the lengths

7. xactxx

you can use cosine rule a^2 = b^2+c^2-2bc cos A for angle B

8. xactxx

you'll get x that way

9. Mimi_x3

Okay, like 40/sin45 = x/sinC ?

10. Mimi_x3

w8 nvm

11. xactxx

40^2 = x^2 + (2x)^2 - 2x(2x) cos 45 1600 = x^2 + 4x^2 - 4x^2 (1/sqrt(2)) 1600 = 5x^2 - 2sqrt(2)x^2 1600 / (5 - 2sqrt(2)) = x^2 x^2 = 736.79 x = sqrt(736.79) = 27.14m So Don is 27.1*2 = 54.2m away from the building and Cindy is 27.1m away from the building.

12. Mimi_x3

Tyvm (:

13. xactxx

btw in the diagram I swapped Cindy and Don, but that's not too much of a problem... the problem works itself out in the same way.

14. Mimi_x3

Okay xD

15. Mimi_x3

Um , I did it and I got x= 47.568 xD

16. xactxx

I still you should still get to the same answer...?

17. Mimi_x3

idk, thats how i did it 1600 = x^2 + 4x^2 - 4x^2 * cos45 1600 = x^2 *cos45 cos45x^2 = 1600 x^2 = 2262.74 x = 47.578 Did I stuff it up somewhere ?

18. xactxx

yes. You first perform multiplication, then subtraction, according to BODMAS. You first applied subtraction and then multiplication!

19. Mimi_x3

Hm, i don't follow the BODMAS thing xD Wonder why I stuffed it up xD but how did I stuff it up ? Since I already subtracted it first

20. xactxx

1600 = x^2 + 4x^2 - 4x^2 * cos 45 You first performed addition and subtraction: 1600 = x^2 * cos 45 when you should have first performed multiplication! 1600 = x^2 + 4x^2 - 2.828x^2

21. Mimi_x3

Where did you get 2.828 from ?

22. xactxx

4 * cos 45

23. Mimi_x3