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Category: Geometry

Question-172628

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Question Number 172628 by mnjuly1970 last updated on 29/Jun/22 Commented by mr W last updated on 29/Jun/22 $${maybe}\:\frac{\mathrm{2}}{\mathrm{tan}\:\gamma}=\frac{\mathrm{1}}{\mathrm{tan}\:\beta}−\frac{\mathrm{1}}{\mathrm{tan}\:\alpha}\:? \\ $$ Commented by mnjuly1970 last updated…

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Question Number 41521 by maxmathsup by imad last updated on 08/Aug/18 $${let}\:{A}\left(−\mathrm{1},\mathrm{1}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{3}\right)\:\:\:{find}\:\:\:{image}\:{of}\:{the}\:{line}\:\left({AB}\right)\:{by} \\ $$$$\left.\mathrm{1}\right)\:{translation}\:{t}_{\overset{\rightarrow} {{u}}} \:\:\:\:{with}\:\overset{\rightarrow} {{u}}\left(\mathrm{1}−\mathrm{2}{i}\right) \\ $$$$\left.\mathrm{2}\right)\:{rotation}\:{R}\left({w},\frac{\pi}{\mathrm{3}}\right)\:\:{with}\:{w}\left(\mathrm{1}+{i}\right) \\ $$ Terms of Service Privacy…

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Two-places-A-and-B-both-on-a-parallel-of-latitude-N-differs-in-longitudes-by-Show-that-the-shortest-distance-between-them-is-2-sin-1-cos-sin-2-360-2piR-Topic-

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Question Number 106990 by I want to learn more last updated on 08/Aug/20 $$\mathrm{Two}\:\mathrm{places}\:\:\mathrm{A}\:\:\mathrm{and}\:\:\mathrm{B}\:\:\mathrm{both}\:\mathrm{on}\:\mathrm{a}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitude}\:\:\alpha°\mathrm{N} \\ $$$$\mathrm{differs}\:\mathrm{in}\:\mathrm{longitudes}\:\mathrm{by}\:\:\theta°.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance} \\ $$$$\mathrm{between}\:\mathrm{them}\:\mathrm{is}:\:\:\:\:\:\frac{\left[\mathrm{2}\:\mathrm{sin}^{−\:\mathrm{1}} \left(\mathrm{cos}\:\alpha\:\mathrm{sin}\:\frac{\theta}{\mathrm{2}}\right)\right]}{\mathrm{360}}\:\:×\:\:\mathrm{2}\pi\mathrm{R} \\ $$$$ \\ $$$$\mathrm{Topic}:\:\:\mathrm{Longitude}\:\mathrm{and}\:\mathrm{Latitude} \\ $$…

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Question-106977

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Question Number 106977 by mr W last updated on 08/Aug/20 Answered by mr W last updated on 08/Aug/20 $${A}\left({a},\mathrm{0}\right)\:{and}\:{B}\left({b},\mathrm{0}\right) \\ $$$${P}\:{lies}\:{on}\:{y}={x}^{\mathrm{2}} \\ $$$${find}\:{the}\:{minimum}\:{of}\:{perimeter}\:{of} \\ $$$$\Delta{PAB}.…

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Question-172484

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Question Number 172484 by mnjuly1970 last updated on 27/Jun/22 Answered by mr W last updated on 28/Jun/22 $${let}\:\theta=\angle{ADC} \\ $$$$\frac{\mathrm{10}}{\mathrm{sin}\:\theta}=\frac{\mathrm{5}}{\mathrm{sin}\:\alpha}=\frac{{AD}}{\mathrm{sin}\:\left(\theta+\alpha\right)} \\ $$$$\frac{\mathrm{6}}{\mathrm{sin}\:\mathrm{2}\alpha}=\frac{{AD}}{\mathrm{sin}\:\left(\theta−\mathrm{2}\alpha\right)} \\ $$$$\mathrm{sin}\:\theta=\mathrm{2}\:\mathrm{sin}\:\alpha \\…

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