Mathematics: Stacy is watching an airplane that is 6 miles away from her and 4 miles above the ground. how many degrees above the horizontal must she look up to see the plane?

Stacy is watching an airplane that is 6 miles away

Ответ:

salmanderabdi12

23.05.2020

I was looking out of my window and saw a plane making a contrail slightly more south west of my ... do I need to work out how far up I am to get a good angle? or is that negated by the fact it is 6 miles up ...

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Ответ:

samiyahbass

10.08.2022

Mathematics

$\bf \textit{ roots of complex numbers, DeMoivre's theorem}
\\\\
\sqrt[n]{z}=\sqrt[n]{r}\left[ cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\ sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad 
\begin{array}{llll}
k\ roots\\
0,1,2,3,...
\end{array}\\\\
-------------------------------\\\\
27[cos(279^o)+i~sin(279^o)]$

$\bf \stackrel{\textit{first root, k = 0}}{\sqrt[3]{27}\left[cos\left( \frac{279+360(0)}{3} \right)+i~ sin\left( \frac{279+360(0)}{3} \right) \right]}
\\\\\\
3\left[cos\left( \frac{279}{3} \right)+i~ sin\left( \frac{279}{3} \right) \right]\implies 
3[cos(93^o)+i~sin(93^o)]
\\\\\\
\boxed{-0.15700787+29958886i}$

$\bf \stackrel{\textit{second root, k = 1}}{\sqrt[3]{27}\left[cos\left( \frac{279+360(1)}{3} \right)+i~ sin\left( \frac{279+360(1)}{3} \right) \right]}
\\\\\\
3\left[cos\left( \frac{639}{3} \right)+i~ sin\left( \frac{639}{3} \right) \right]\implies 
3[cos(213^o)+i~sin(213^o)]
\\\\\\
\boxed{-2.5160117-1.633917i}$

$\bf \stackrel{\textit{third root, k = 2}}{\sqrt[3]{27}\left[cos\left( \frac{279+360(2)}{3} \right)+i~ sin\left( \frac{279+360(2)}{3} \right) \right]}
\\\\\\
3\left[cos\left( \frac{999}{3} \right)+i~ sin\left( \frac{999}{3} \right) \right]\implies 
3[cos(333^o)+i~sin(333^o)]
\\\\\\
\boxed{2.67301957-1.3619715i}$

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Stacy is watching an airplane that is 6 miles away from her and 4 miles above the ground. how many degrees above the horizontal must she look up to see the plane?

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