Two wires tether a balloon to the ground as shown, how high is the balloon above the ground? I've done it twice..

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Two wires tether a balloon to the ground as shown, how high is the balloon above the ground? I've done it twice..

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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is that correct?
the answer I keep getting for height = 371.78 but that's not correct o.0
|dw:1434517128031:dw| I would solve it this way: \[\large \tan 75=\frac{h}{100+x}\ ..........(1)\] \[\large \tan 85=\frac{h}{x}\ .........(2)\] Rearranging (2) we get: \[\large x=\frac{h}{\tan 85}\ ..........(3)\] Plugging the value for x from (3) into (1) gives: \[\large \tan 75=\frac{h}{100+\frac{h}{\tan 85}}\ ..........(4)\] Now solve (4) to find the value of h.
Equation (4) rearranges to give: \[\large 100 \tan 75 +\frac{h \tan 75}{\tan 85}=h\ ..........(5)\] Can you solve h?
Um.. 373.205+ (htan(75))/11.43
How do I solve for h if h is in the left side as well?
Putting values into (5) we get: \[\large 373.2+0.3265h=h\ ........(6)\] Subtracting 0.3265h from both sides gives: \[\large 0.6735h=373.2\ ..........(7)\]
You mean 0.6735h= - 373.2 (notice this side is negative)
How did you get 0.6735?
No, 373.2 is not negative. \[\large \frac{h \tan 75}{\tan 85}=0.3265h\]
sorry, I got lost on part 7 We have 373+0.32658h=h (6) if we subtract 0.32658h from both sides we would get 373=h-0.32658h
373=h-0.32658h 1.00000h -0.32658h=?
Ah, gotcha. Ok :P
Cool!
So now we divide 373 by 0.6735
Correct.
and get 554, which is the correct answer :P
what was I doing that was wrong?! o.o
You needed to form a pair of simultaneous equations to solve this question. Notice I added another variable x to the drawing. Of course we do not need to find the value of x (although we could by substitution).
Right, I used tan first and then used the Law of Sines..
Your equation tan (theta) = y/100 is not understood by me. Where is y in the drawing?
ai, I meant tan(theta)=x/100
|dw:1434519774006:dw| tan(75)=x/100 100tan75)=373.205 Then I did the law of sines a/(sin85) = x/sin90 a= (xsin85)/(sin(90)) so the height = 371.78
The equation for finding the x? to use tangent It needs to be a right triangle?
The triangle with x, 75 degrees and a side length of 100 units is not a right angled triangle. Therefore your equation is not valid.
In your usage of tan in a triangle, the triangle must be a right-angled type.
oh gosh, I didn't know that. That's really good to know o.0
You're welcome :)
ok, thanks :)

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