cutiecomittee123 one year ago Find the measure of angle b find x find y

1. cutiecomittee123

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2. jim_thompson5910

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3. jim_thompson5910

using A as a reference angle, we can add these labels |dw:1441846105403:dw|

4. jim_thompson5910

find x and y using the trig ratios then find angle B

5. cutiecomittee123

okay

6. cutiecomittee123

i need more pointers, @jim_thompson5910

7. anonymous

still doing hw huh

8. anonymous

angle b= 165

9. anonymous

nvm

10. anonymous

im tired.

11. jim_thompson5910

how far did you get @cutiecomittee123 based on the info I posted?

12. cutiecomittee123

no where lol let me try again

13. cutiecomittee123

well i kind of took the easy way out and I just figured there are 180 degrees in a triangle and it is given 90+75 so i added them and got 165 then if you add 15 you get 180 so obviousely angle b is 15 degrees. but then to solve for x and y i can easily see that you just use the trig stuff

14. jim_thompson5910

yes B = 15 degrees

15. jim_thompson5910

how would you find x?

16. cutiecomittee123

I am having a brain fart and cant remeber

17. jim_thompson5910

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18. jim_thompson5910

which angle do you want to use? A = 75? or B = 15?

19. cutiecomittee123

well lets use B, and wouldnt you use cos because you would do adjacent over hypotenuse? So it would be cos(15)=125/y

20. jim_thompson5910

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21. jim_thompson5910

cos(B) = adjacent/hypotenuse cos(15) = 125/x now solve for x

22. cutiecomittee123

So wouldnt you take the inverse of both sides?

23. cutiecomittee123

sorry for the super late replies i am also working on a power point.

24. jim_thompson5910

it's ok, work on the powerpoint first and we can work on this later

25. cutiecomittee123

Alright done with the presentation, lets do this:)

26. jim_thompson5910

so you see how I got cos(15) = 125/x right?

27. cutiecomittee123

yes

28. jim_thompson5910

using a calculator, what is the value of cos(15) equal to (in terms of a decimal number)

29. cutiecomittee123

cos(15)=.97

30. jim_thompson5910

so what we really have is 0.97 = 125/x are you able to solve that for x?

31. cutiecomittee123

hmm, multiply both sides by x?

32. jim_thompson5910

then what

33. cutiecomittee123

divide by .97

34. jim_thompson5910

yes

35. cutiecomittee123

on both sides

36. jim_thompson5910

what is x equal to

37. cutiecomittee123

x=128.87

38. jim_thompson5910

ok so 125/0.97 = 128.87 is correct it turns out that 125/(cos(15)) = 129.40952255126 is the more accurate answer so it might be best to type into your calculator 125/(cos(15))

39. cutiecomittee123

okay cool got it, but why would you divide it form 125?

40. jim_thompson5910

$\Large \cos(15^{\circ}) = \frac{125}{x}$ $\Large \cos(15^{\circ})\color{red}{*x} = \frac{125}{x}\color{red}{*x}$ $\Large \cos(15^{\circ})\color{black}{*x} = \frac{125}{\cancel{x}}\color{black}{*\cancel{x}}$ $\Large \cos(15^{\circ})*x = 125$ $\Large \frac{\cos(15^{\circ})*x}{\color{red}{\cos(15^{\circ})}} = \frac{125}{\color{red}{\cos(15^{\circ})}}$ $\Large \frac{\cancel{\cos(15^{\circ})}*x}{\cancel{\cos(15^{\circ})}} = \frac{125}{\color{black}{\cos(15^{\circ})}}$ $\Large x = \frac{125}{\color{black}{\cos(15^{\circ})}}$

41. jim_thompson5910

So what I first did was multiply both sides by x then I divided both sides by cos(15)

42. cutiecomittee123

i see you just solved it like an algebraic equation, basic algebra

43. jim_thompson5910

yeah if you have to, think of cos(15) as y so you'd have y = 125/x solving for x gives x = 125/y

44. cutiecomittee123

okay woah, so now y=129.41 and then we can just use the pythagorean theorum to solve for x. so 129.41^2+125^2=x^ added together i get 32302.1396 the square root of that is 179.72796 so x=179.73

45. jim_thompson5910

no, I let y = cos(15) so y = 0.97 like you got, but it's best to leave the cos(15) part alone as it is

46. jim_thompson5910

if you typed 125/cos(15) into a calculator, what do you get?

47. cutiecomittee123

I get 129.41

48. jim_thompson5910

yes, 125/cos(15) = 129.40952255126

49. cutiecomittee123

which is what the side y is equal to

50. jim_thompson5910

oh my bad, I picked y when y is already being used in the drawing

51. cutiecomittee123

yeah lol oops. but yes I think we have it all figured out now. thanks so much!!!!

52. jim_thompson5910

you're welcome