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?

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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
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|dw:1436226077507:dw|
you want to find the distance the shuttle has gone up when her angle of elevation us 80 deg
you are given she is 6 miles away from the shuttle launch

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use the given and the thing you want to find to express a trigonometric equation to solve
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?
I honestly have no idea... I don't even what a trigonometric ratio is
that is weird so you never heard so sin,cos,tan,csc,sec,cot?
I know sin cos and tan
and do you know that tan(of an angle) is the opposite side of that angle divided by the adjacent side of that angle?
yea
ok so that is the trigonometric ratio you want to use
here is an easy solution if you know tan and sin|dw:1436226242655:dw| use the angle of 10 with the tan ratio
notice as I said before you are given the adjacent side and looking for the opposite side of the angle 80 deg
@campbell_st where did you get 10 from?
the sum of the angles of a triangle equal 180 deg
90+80+what=180
oh ok i gotcha
so would it be 80/10
no
sin cos tan are ratios of sides of angle
i don't understand this
tan(80)=(opp SIDE of angle with measurement 80) divided by (adj SIDE of angle with measurement 80)
need hlp to
|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 ?
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opposite - 10 ? adjacent - 6 ?
adjacent is right but how are you getting the opp is 10?
is it x
|dw:1436226982237:dw|
\[\tan(80^o)=\frac{x}{6}\] great now solve this for x
How do i solve for x
you undo the division there by x do you see that x is being divided by 6?
try multiplying by 6 on both sides to get x by itself
would it be tan80 * 6?
yes x=6*tan(80) just whip out your calculator and type that in to find what x is
34.02
I would probably round to 34.03 since there is a 7 behind that 2
yea sorry about that lol
you could have used the angle mentioned by campbell too
the setup would have looked different but should end up with same answer
\[\tan(10^o)=\frac{6}{x} \\ \frac{1}{\tan(10^o)}=\frac{x}{6} \\ \frac{6}{ \tan(10^o)}=x\]
this also gives you 34.03
ahh ok thanks :)
np
i have more questions if you dont mind helping lol
I might be able to help with one more. You might also find this site helpful https://www.mathsisfun.com/sine-cosine-tangent.html
like have you ever heard of soh cah toa?
it is an easy way to remember trig ratios for sin,cos,and tan
yea i do
soh cah toa s=o/h c=a/h t=o/a
anyways post another question if you have issues
can you tell me what geometric mean is
oh the geometric mean of a and b is : \[\sqrt{a \cdot b}\] in general the geometric means of \[x_1,x_2,... ,x_n \text{ is } \sqrt[n]{x_1 \cdot x_2 \cdots x_n}\]
Find the geometric mean between 14 & 21. this is the questoin
well that fits in with that first formula nicely since like that one you have two numbers
just replace a with 14 and b with 21
and simplify
\[\sqrt{294}\] ?
how do you simplify
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) \[\sqrt{21 \cdot 14} \\ =\sqrt{7^2 \cdot 2(3)} \\ =\sqrt{7^2} \sqrt{2(3)}\]
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
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
just curious you don't know the sqrt(7^2)?

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