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Category: Geometry

Let-the-triangle-A-3-2-B-8-4-C-4-6-solve-a-find-the-perimeter-b-find-the-area-c-find-the-base-d-find-the-height-e-classify-it-

Question Number 167073 by neinhaltsieger369 last updated on 05/Mar/22 $$\:\boldsymbol{\mathrm{Let}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{triangle}}\:\:\boldsymbol{\mathrm{A}}\left(−\mathrm{3};\:\mathrm{2}\right),\:\:\boldsymbol{\mathrm{B}}\left(\mathrm{8};\:\mathrm{4}\right),\:\:\boldsymbol{\mathrm{C}}\left(\mathrm{4};\:−\mathrm{6}\right),\:\:\boldsymbol{\mathrm{solve}}\underset{\:} {\overset{\:} {:}} \\ $$$$\:\left(\boldsymbol{\mathrm{a}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{perimeter}}; \\ $$$$\:\left(\boldsymbol{\mathrm{b}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{area}}; \\ $$$$\:\left(\boldsymbol{\mathrm{c}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{base}}; \\ $$$$\:\left(\boldsymbol{\mathrm{d}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{height}}; \\…

Question-167043

Question Number 167043 by mnjuly1970 last updated on 05/Mar/22 Answered by mr W last updated on 05/Mar/22 $${say}\:\angle{B}=\beta \\ $$$$\mathrm{tan}\:\beta=\frac{\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\alpha}{\mathrm{4}−\mathrm{3}\:\mathrm{cos}\:\mathrm{2}\alpha}=\frac{\mathrm{6}\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\alpha}{\mathrm{1}+\mathrm{6}\:\mathrm{sin}^{\mathrm{2}} \:\alpha} \\ $$$$\frac{\mathrm{sin}\:\beta}{\mathrm{6}}=\frac{\mathrm{sin}\:\alpha}{\mathrm{4}}\:\Rightarrow\mathrm{sin}\:\beta=\frac{\mathrm{3}\:\mathrm{sin}\:\alpha}{\mathrm{2}} \\ $$$$\left(\frac{\mathrm{6}\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\alpha}{\mathrm{1}+\mathrm{6}\:\mathrm{sin}^{\mathrm{2}}…

Question-167011

Question Number 167011 by mnjuly1970 last updated on 04/Mar/22 Answered by TheSupreme last updated on 04/Mar/22 $${Talete}\:{theorem}\:{respect}\:{point}\:{A}\:{far}\:{away}\:{x}\:{from}\:{center}\: \\ $$$${of}\:{circle}\:{of}\:{radius}\:\mathrm{4} \\ $$$${let}'{s}\:{y}={PQ} \\ $$$${x}:\mathrm{4}=\left({x}+\mathrm{4}\right):{y}=\left({x}+\mathrm{12}\right):\mathrm{8} \\ $$$$\frac{{x}}{\mathrm{4}}=\frac{{x}+\mathrm{12}}{\mathrm{8}}\rightarrow{x}=\mathrm{12}…

new-idea-and-solution-to-questions-35178-amp-35195-triangle-ABC-a-BC-b-CA-c-AB-CAB-ABC-BCA-d-a-b-c-a-b-c-a-b-c-a-b-c-put-it-as-this-A-0-0-B-c-0-C-

Question Number 35871 by MJS last updated on 25/May/18 $$\mathrm{new}\:\mathrm{idea}\:\left(\mathrm{and}\:\mathrm{solution}\right)\:\mathrm{to}\:\mathrm{questions}\:\mathrm{35178}\:\&\:\:\mathrm{35195} \\ $$$$ \\ $$$$\mathrm{triangle}: \\ $$$${ABC};\:{a}={BC},\:{b}={CA},\:{c}={AB}; \\ $$$$\alpha=\angle{CAB},\:\beta=\angle{ABC},\:\gamma=\angle{BCA} \\ $$$${d}=\sqrt{\left({a}+{b}+{c}\right)\left({a}+{b}−{c}\right)\left({a}−{b}+{c}\right)\left(−{a}+{b}+{c}\right)} \\ $$$$ \\ $$$$\mathrm{put}\:\mathrm{it}\:\mathrm{as}\:\mathrm{this}: \\…