## Ammarah 2 years ago how do u know when to use sin and cos?

1. Ammarah

@mathstudent55

2. IsTim

sin for opposite over hypotenus cos for adjacent over hypotenus

3. Ammarah

I know but like in a problem...i dont get which one i should use

4. Ammarah

Use a sine or cosine ration to find the value of each variable. Round decimals to the nearest tenth.

5. Ammarah

|dw:1358230193689:dw|

6. Ammarah

7. Ammarah

i dont get them

8. IsTim
9. IsTim

use that. sorry. i ahve to go soon.

10. Ammarah

it doesnt help please solve these for me

11. Callisto

|dw:1358230939592:dw| Refer to the reference angle. Sin => opposite side (to the reference angle) / hypotenuse In this diagram, can you determine what sine theta is?

12. Ammarah

? no

13. Callisto

what is the opposite side to the reference angle theta?

14. Ammarah

x

15. Callisto

and what is the hypotenuse?

16. Ammarah

2 btw what is theta?

17. Callisto

Sorry :| that was supposed to be z :| If you know x and z, you can find theta. Because sin (theta) = x/z Got it?

18. opiesche

Ammara, so in an equation, Callisto is saying is that in the figure above, $\sin(\theta) = \frac{ x }{ z }$ So, in your figure, the first problem: you know the hypotenuse (18) and the angle opposite x (32 degrees). So you know that, $\sin(32) = \frac{ x }{ 18 }$ Then solve for x :)

19. opiesche

And that's the sine of 32 degrees of course, not radians.

20. Ammarah

what do i do for why then?

21. Ammarah

|dw:1358231828749:dw|

22. opiesche

Well, you know that the angle opposite x is 32 degrees, and that the angle opposite the hypotentuse is 90 degrees. You also know the total sum of all interior angles of a triangle - so from that you can figure out the remaining angle you don't know, and do the same thing.

23. Ammarah

i dont get it....how to i solve for y?

24. Ammarah

and does x=9.5?

25. opiesche

Or alternatively, use the cosine which is the adjacent angle over the hypotenuse: $\cos(\theta) = \frac{ y }{ z }$ Substitute for the adjacent angle (32 degrees again) and for the hypotenuse (18), and solve for y the same way you solved for x above.

26. Ammarah

|dw:1358232234127:dw|

27. opiesche

Correct.

28. Ammarah

Ok how about the next triangle...

29. Ammarah

|dw:1358232364105:dw|

30. Ammarah

|dw:1358232378783:dw|

31. Ammarah

so in the left triangle were solving for a.

32. Ammarah

how would u solve it? please solve it for me.......

33. opiesche

Correct. And you know that the cosine of the angle (48 degrees) is the same as 10 divided by a - careful here, because a is the hypotenuse: $\cos(\Theta) = \frac{ 10 }{ a }$ So, $\cos(48) = \frac{ 10 }{ a }$

34. Ammarah

how would i solve be now...i got 14.9 for a

35. opiesche

That's correct. Now solve the last figure?

36. Ammarah

b=11.1?

37. opiesche

Yes!

38. opiesche

You got it. Can you do the last triangle?