## anonymous one year ago Anna is watching a space shuttle launch 6 miles from Cape Canaveral in Florida. When the angle of elevation from her viewpoint to the shuttle is 80 degrees, how high is the shuttle if it is going straight up?

1. freckles

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2. freckles

you want to find the distance the shuttle has gone up when her angle of elevation us 80 deg

3. freckles

you are given she is 6 miles away from the shuttle launch

4. freckles

use the given and the thing you want to find to express a trigonometric equation to solve

5. freckles

for example you are given the adjacent side to the angle given and you are ask to find the opp site this just screams what trig ratio?

6. anonymous

I honestly have no idea... I don't even what a trigonometric ratio is

7. freckles

that is weird so you never heard so sin,cos,tan,csc,sec,cot?

8. anonymous

I know sin cos and tan

9. freckles

and do you know that tan(of an angle) is the opposite side of that angle divided by the adjacent side of that angle?

10. anonymous

yea

11. freckles

ok so that is the trigonometric ratio you want to use

12. campbell_st

here is an easy solution if you know tan and sin|dw:1436226242655:dw| use the angle of 10 with the tan ratio

13. freckles

notice as I said before you are given the adjacent side and looking for the opposite side of the angle 80 deg

14. anonymous

@campbell_st where did you get 10 from?

15. freckles

the sum of the angles of a triangle equal 180 deg

16. freckles

90+80+what=180

17. anonymous

oh ok i gotcha

18. anonymous

so would it be 80/10

19. freckles

no

20. freckles

sin cos tan are ratios of sides of angle

21. anonymous

i don't understand this

22. freckles

tan(80)=(opp SIDE of angle with measurement 80) divided by (adj SIDE of angle with measurement 80)

23. anonymous

need hlp to

24. freckles

|dw:1436226787960:dw| $\tan(80^o)=\frac{\text{ opp side }}{\text{ adj side }}$|dw:1436226852206:dw| can you identify the sides that are opposite and adjacent ?

25. anonymous

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26. anonymous

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27. anonymous

opposite - 10 ? adjacent - 6 ?

28. freckles

adjacent is right but how are you getting the opp is 10?

29. anonymous

is it x

30. freckles

|dw:1436226982237:dw|

31. freckles

$\tan(80^o)=\frac{x}{6}$ great now solve this for x

32. anonymous

How do i solve for x

33. freckles

you undo the division there by x do you see that x is being divided by 6?

34. freckles

try multiplying by 6 on both sides to get x by itself

35. anonymous

would it be tan80 * 6?

36. freckles

yes x=6*tan(80) just whip out your calculator and type that in to find what x is

37. anonymous

34.02

38. freckles

I would probably round to 34.03 since there is a 7 behind that 2

39. anonymous

40. freckles

you could have used the angle mentioned by campbell too

41. freckles

the setup would have looked different but should end up with same answer

42. freckles

$\tan(10^o)=\frac{6}{x} \\ \frac{1}{\tan(10^o)}=\frac{x}{6} \\ \frac{6}{ \tan(10^o)}=x$

43. freckles

this also gives you 34.03

44. anonymous

ahh ok thanks :)

45. freckles

np

46. anonymous

i have more questions if you dont mind helping lol

47. freckles

I might be able to help with one more. You might also find this site helpful https://www.mathsisfun.com/sine-cosine-tangent.html

48. freckles

like have you ever heard of soh cah toa?

49. freckles

it is an easy way to remember trig ratios for sin,cos,and tan

50. anonymous

yea i do

51. freckles

soh cah toa s=o/h c=a/h t=o/a

52. freckles

anyways post another question if you have issues

53. anonymous

can you tell me what geometric mean is

54. freckles

oh the geometric mean of a and b is : $\sqrt{a \cdot b}$ in general the geometric means of $x_1,x_2,... ,x_n \text{ is } \sqrt[n]{x_1 \cdot x_2 \cdots x_n}$

55. anonymous

Find the geometric mean between 14 & 21. this is the questoin

56. freckles

well that fits in with that first formula nicely since like that one you have two numbers

57. freckles

just replace a with 14 and b with 21

58. freckles

and simplify

59. anonymous

$\sqrt{294}$ ?

60. anonymous

how do you simplify

61. freckles

that is right but that could be simplified I would have left 294 as 21*14 and looked for perfect square factors for example I know 21=7*3 and 14=7*2 so 21*14=2*3*7^2 and you know the square root of 7^2 (aka 49) $\sqrt{21 \cdot 14} \\ =\sqrt{7^2 \cdot 2(3)} \\ =\sqrt{7^2} \sqrt{2(3)}$

62. anonymous

Select one: a. 103√ or appx. 17.3 b. 17.5 c. 76√ or appx. 17.1 d. 637/35 or appx. 18.2 these are the answers

63. freckles