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Category: Geometry

Question-39993

Question Number 39993 by ajfour last updated on 14/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 14/Jul/18 $${let}\:\angle{AOT}=\theta \\ $$$${OT}\parallel\:{toBC}\:{so}\:\frac{{AO}}{{AC}}=\frac{{AT}}{{AB}}=\frac{{OT}}{{BC}} \\ $$$${point}\:{T}\left({cos}\theta,{sin}\theta\right)\:\:{andpoint}\:{C}\left(−\mathrm{1},\mathrm{0}\right) \\ $$$${eqn}\:\:\:{of}\:{OT}\:{is}\:{y}={xtan}\theta \\ $$$${eqn}\:{ofCB}\:{is}\:{y}=\left({x}+\mathrm{1}\right){tan}\theta…

Question-39985

Question Number 39985 by ajfour last updated on 14/Jul/18 Answered by ajfour last updated on 15/Jul/18 $${eq}.\:{of}\:{line}\:\:{OBC}\::\:\:{y}={x} \\ $$$${eq}.\:{of}\:{AEC}:\:\:\:\:{y}\mathrm{tan}\:\theta={x}−\mathrm{1} \\ $$$${For}\:{point}\:{C}\:: \\ $$$$\:\:\:\:\:{x}_{{C}} ={y}_{{C}} =\frac{\mathrm{1}}{\mathrm{1}−\mathrm{tan}\:\theta}\:\:…

Question-39854

Question Number 39854 by ajfour last updated on 12/Jul/18 Commented by ajfour last updated on 12/Jul/18 $${Choose}\:{the}\:{correct}\:{options}: \\ $$$$\left({i}\right)\:{a}\approx\mathrm{1}.\mathrm{6}\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\:{b}\approx\mathrm{2}.\mathrm{7} \\ $$$$\left({iii}\right)\:\:{a}\:\approx\:\mathrm{1}.\mathrm{8}\:\:\:\left({iv}\right)\:\:{b}\:\approx\:\mathrm{2}.\mathrm{4} \\ $$$$ \\ $$…

Question-39848

Question Number 39848 by ajfour last updated on 12/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 12/Jul/18 $${tan}\theta=\frac{{a}}{\mathrm{1}} \\ $$$${sin}\theta=\frac{\mathrm{1}}{\mathrm{1}+{a}} \\ $$$${tan}\theta=\frac{{a}}{\mathrm{1}}\:\:{so}\:{sin}\theta=\frac{{a}}{\:\sqrt{\mathrm{1}+{a}^{\mathrm{2}} }} \\ $$$$\frac{{a}}{\:\sqrt{\mathrm{1}+{a}^{\mathrm{2}} }}=\frac{\mathrm{1}}{{a}+\mathrm{1}}…

Question-39678

Question Number 39678 by ajfour last updated on 09/Jul/18 Commented by ajfour last updated on 09/Jul/18 $$\bigtriangleup{ABC}\:{is}\:{projection}\:{of}\:{an}\: \\ $$$${equilateral}\:\bigtriangleup{APQ}.\:{Find}\:{the}\: \\ $$$${height}\:{p},{q}\:{of}\:{vertices}\:{P}\:{and}\:{Q} \\ $$$${above}\:{ground}\:{in}\:{terms}\:{of}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}. \\ $$…

Question-39666

Question Number 39666 by ajfour last updated on 09/Jul/18 Commented by ajfour last updated on 09/Jul/18 $${In}\:{terms}\:{of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{\theta}\:,\:{find}\: \\ $$$$\:\boldsymbol{{x}},\:\boldsymbol{{y}},\:\boldsymbol{\alpha},\:\boldsymbol{\beta},\:{and}\:\boldsymbol{{r}}\:.\:\:\:\left({y}=\:{AD}\right) \\ $$ Answered by tanmay.chaudhury50@gmail.com last…