User:DrBeWa/sandbox

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Cite web

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date: 2024-11-04 -- |accessdate=4 November 2024 -- |date=20 May 2010 -- x ^[1] . . ^[2] . .

^ "t". w. 15 May 1996. Retrieved 3 January 2016.
^ "Mathematical Bridge, List entry number 1125515". The National Heritage List for England. English Heritage. 1950-04-27. Retrieved 2012-11-02.

Cite web w/ archiveurl

Help:Using the Wayback Machine, Template:Cite web, Usage/copy-and-paste, Examples, Wizzard for this template: Templator

date: 2024-11-04 -- |accessdate=4 November 2024 -- |archive-date=19 March 2015 ^[1] . .

^ "List of all prize recipients 1986-2015" (PDF) (in German). Deutsche Forschungsgemeinschaft. 2015. Archived from the original (PDF) on 19 March 2015. Retrieved 2 January 2016.

Details

Template:Details

Fiddling

{\begin{aligned}-2x&&\;+\;&&y&&\;+\;&&2z&&\;=\;&&-3&\qquad (L_{3}){\text{xx}}\end{aligned}}

Calculation

Triangulation may be used to calculate the coordinates and distance from the shore to the ship.

\ell =\ell _{1}+\ell _{2},~~~\tan \alpha ={\frac {d}{\ell _{1}}}~\Rightarrow ~\ell _{1}={\frac {d}{\tan \alpha }}

\ell ={\frac {d}{\tan \alpha }}+{\frac {d}{\tan \beta }}

Therefore

d=\ell \,/\,({\tfrac {1}{\tan \alpha }}+{\tfrac {1}{\tan \beta }})

Using the trigonometric identities tan α = sin α / cos α and sin(α + β) = sin α cos β + cos α sin β, this is equivalent to:

d={\frac {\ell \sin \alpha \sin \beta }{\sin(\alpha +\beta )}}

From this, it is easy to determine the distance of the unknown point from either observation point, its north/south and east/west offsets from the observation point, and finally its full coordinates.

[1] "t". w. 15 May 1996. Retrieved 3 January 2016.

[2] "Mathematical Bridge, List entry number 1125515". The National Heritage List for England. English Heritage. 1950-04-27. Retrieved 2012-11-02.

[3] "List of all prize recipients 1986-2015" (PDF) (in German). Deutsche Forschungsgemeinschaft. 2015. Archived from the original (PDF) on 19 March 2015. Retrieved 2 January 2016.

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