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Category: Geometry

if-are-the-angles-of-a-triangle-find-sin-2-sin-2-sin-2-sin-sin-sin-

Question Number 158391 by mr W last updated on 03/Nov/21 $${if}\:\alpha,\beta,\gamma\:{are}\:{the}\:{angles}\:{of}\:{a}\:{triangle}, \\ $$$${find}\:\frac{\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\alpha}+\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\beta}+\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\gamma}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\beta}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\gamma}}=? \\ $$ Commented by MJS_new last updated on 03/Nov/21 $$\mathrm{4} \\ $$…

if-are-the-angles-of-a-triangle-find-1-tan-tan-1-tan-tan-1-tan-tan-

Question Number 158335 by mr W last updated on 02/Nov/21 $${if}\:\alpha,\beta,\gamma\:{are}\:{the}\:{angles}\:{of}\:{a}\:{triangle}, \\ $$$${find}\: \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{\beta}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\beta}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{\gamma}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\gamma}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{\alpha}}=? \\ $$ Answered by puissant last updated on 03/Nov/21 $$\:\:\:\:\:\:\:\:\:\:\:\alpha\:+\:\beta\:+\:\gamma\:=\:\pi\:\rightarrow\:\alpha\:+\:\beta\:=\:\pi−\gamma\:;…

y-y-1-m-x-x-1-y-1-5-x-2-y-1-5x-10-y-5x-10-1-y-5x-9-

Question Number 92743 by romariocg11 last updated on 09/May/20 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:\:−\:\:{y}_{\mathrm{1}} \:\:=\:\:{m}\:\left(\:{x}\:−\:{x}_{\mathrm{1}} \:\right) \\ $$$$\:\:\:\Rightarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:−\:\mathrm{1}\:=\:\:\mathrm{5}\:\left(\:{x}\:−\:\mathrm{2}\:\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:−\:\mathrm{1}\:=\:\:\mathrm{5}{x}\:−\:\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:=\:\:\mathrm{5}{x}\:−\:\mathrm{10}\:+\:\mathrm{1} \\…

Question-158079

Question Number 158079 by ajfour last updated on 30/Oct/21 Commented by ajfour last updated on 31/Oct/21 $${Sir},\:{the}\:{question}\:{should}\:{state}: \\ $$$${find}\:{sum}\:{of}\:{radii}\:\left({in}\:{terms}\:{of}\right. \\ $$$$\left.{sides}\:{of}\:\bigtriangleup{ABC}\right)\:{that}\:{touch} \\ $$$${two}\:{sides}\:{of}\:{the}\:{said}\:\bigtriangleup{ABC} \\ $$$${and}\:{outer}\:{sides}\:{of}\:{right}\:{angled}…