anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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freckles
  • freckles
|dw:1436226077507:dw|
freckles
  • freckles
you want to find the distance the shuttle has gone up when her angle of elevation us 80 deg
freckles
  • freckles
you are given she is 6 miles away from the shuttle launch

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freckles
  • freckles
use the given and the thing you want to find to express a trigonometric equation to solve
freckles
  • 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?
anonymous
  • anonymous
I honestly have no idea... I don't even what a trigonometric ratio is
freckles
  • freckles
that is weird so you never heard so sin,cos,tan,csc,sec,cot?
anonymous
  • anonymous
I know sin cos and tan
freckles
  • 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?
anonymous
  • anonymous
yea
freckles
  • freckles
ok so that is the trigonometric ratio you want to use
campbell_st
  • 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
freckles
  • freckles
notice as I said before you are given the adjacent side and looking for the opposite side of the angle 80 deg
anonymous
  • anonymous
@campbell_st where did you get 10 from?
freckles
  • freckles
the sum of the angles of a triangle equal 180 deg
freckles
  • freckles
90+80+what=180
anonymous
  • anonymous
oh ok i gotcha
anonymous
  • anonymous
so would it be 80/10
freckles
  • freckles
no
freckles
  • freckles
sin cos tan are ratios of sides of angle
anonymous
  • anonymous
i don't understand this
freckles
  • freckles
tan(80)=(opp SIDE of angle with measurement 80) divided by (adj SIDE of angle with measurement 80)
anonymous
  • anonymous
need hlp to
freckles
  • 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 ?
anonymous
  • anonymous
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anonymous
  • anonymous
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anonymous
  • anonymous
opposite - 10 ? adjacent - 6 ?
freckles
  • freckles
adjacent is right but how are you getting the opp is 10?
anonymous
  • anonymous
is it x
freckles
  • freckles
|dw:1436226982237:dw|
freckles
  • freckles
\[\tan(80^o)=\frac{x}{6}\] great now solve this for x
anonymous
  • anonymous
How do i solve for x
freckles
  • freckles
you undo the division there by x do you see that x is being divided by 6?
freckles
  • freckles
try multiplying by 6 on both sides to get x by itself
anonymous
  • anonymous
would it be tan80 * 6?
freckles
  • freckles
yes x=6*tan(80) just whip out your calculator and type that in to find what x is
anonymous
  • anonymous
34.02
freckles
  • freckles
I would probably round to 34.03 since there is a 7 behind that 2
anonymous
  • anonymous
yea sorry about that lol
freckles
  • freckles
you could have used the angle mentioned by campbell too
freckles
  • freckles
the setup would have looked different but should end up with same answer
freckles
  • freckles
\[\tan(10^o)=\frac{6}{x} \\ \frac{1}{\tan(10^o)}=\frac{x}{6} \\ \frac{6}{ \tan(10^o)}=x\]
freckles
  • freckles
this also gives you 34.03
anonymous
  • anonymous
ahh ok thanks :)
freckles
  • freckles
np
anonymous
  • anonymous
i have more questions if you dont mind helping lol
freckles
  • 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
freckles
  • freckles
like have you ever heard of soh cah toa?
freckles
  • freckles
it is an easy way to remember trig ratios for sin,cos,and tan
anonymous
  • anonymous
yea i do
freckles
  • freckles
soh cah toa s=o/h c=a/h t=o/a
freckles
  • freckles
anyways post another question if you have issues
anonymous
  • anonymous
can you tell me what geometric mean is
freckles
  • freckles
oh the geometric mean of a and b is : \[\sqrt{a \cdot b}\] in general the geometric means of \[x_1,x_2,... ,x_n \text{ is } \sqrt[n]{x_1 \cdot x_2 \cdots x_n}\]
anonymous
  • anonymous
Find the geometric mean between 14 & 21. this is the questoin
freckles
  • freckles
well that fits in with that first formula nicely since like that one you have two numbers
freckles
  • freckles
just replace a with 14 and b with 21
freckles
  • freckles
and simplify
anonymous
  • anonymous
\[\sqrt{294}\] ?
anonymous
  • anonymous
how do you simplify
freckles
  • 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) \[\sqrt{21 \cdot 14} \\ =\sqrt{7^2 \cdot 2(3)} \\ =\sqrt{7^2} \sqrt{2(3)}\]
anonymous
  • 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
freckles
  • freckles
can't read those answers too well but if you are looking for an approximation instead of a simplified exact answer then plug in sqrt(14*21) into your calculator
freckles
  • freckles
just curious you don't know the sqrt(7^2)?

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