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Category: Geometry

Find-the-number-of-sides-of-two-regular-polygons-that-their-sides-has-a-ratio-5-4-and-of-9-as-a-difference-between-their-angles-

Question Number 182474 by Acem last updated on 10/Dec/22 $${Find}\:{the}\:{number}\:{of}\:{sides}\:{of}\:{two}\:{regular}\:{polygons} \\ $$$$\:{that}\:{their}\:{sides}\:{has}\:{a}\:{ratio}\:\mathrm{5}:\mathrm{4}\:{and}\:{of}\:\mathrm{9}°\:{as}\:{a} \\ $$$$\:{difference}\:{between}\:{their}\:{angles}. \\ $$ Answered by mr W last updated on 10/Dec/22 $${n}−{sided}\:{regular}\:{polygon}:…

Question-182407

Question Number 182407 by Acem last updated on 09/Dec/22 Answered by a.lgnaoui last updated on 09/Dec/22 $${Area}=\mathrm{AC}×\mathrm{AB}\frac{\mathrm{sin}\:\beta}{\mathrm{2}} \\ $$$$\beta=\frac{\mathrm{12}}{\mathrm{5}}\:\mathrm{x}\:\:\:\gamma=\frac{\mathrm{3x}}{\mathrm{2}}\:\:\:\alpha=\frac{\mathrm{3}}{\mathrm{5}}\mathrm{x}\:\:\:\left({degre}\right) \\ $$$$\alpha+\beta+\gamma=\mathrm{180}\:\:\:\left(\:\frac{\mathrm{45}}{\mathrm{10}}\right)×\mathrm{x}=\mathrm{180}\:\:\mathrm{x}=\mathrm{40} \\ $$$$\beta=\frac{\mathrm{12}×\mathrm{40}}{\mathrm{5}}=\mathrm{96}° \\ $$$${Area}=\frac{\mathrm{2}×\mathrm{AB}}{\mathrm{2}}×\mathrm{sin}\:\mathrm{96}…

Question-182375

Question Number 182375 by Acem last updated on 08/Dec/22 Commented by Acem last updated on 08/Dec/22 $$\:{I}\:{just}\:{solved}\:{it},\:\mathrm{2}\:{sec}\:{ago},\: \\ $$$$\left.\:\phi\:\in\:\right]\mathrm{20},\:\mathrm{27}\left[\right. \\ $$$$\:{Btw}\:{extend}\:{of}\:{NA}\:{intersects}\:{with}\:{extend}\:{of}\:{PC} \\ $$$$\:{at}\:{point}\:\in\:{this}\:{circle} \\ $$$$\:{Hope}\:{you}\:{success}\:{to}\:{find}\:\phi\:!…

Question-116800

Question Number 116800 by mr W last updated on 06/Oct/20 Answered by bobhans last updated on 07/Oct/20 $$\Rightarrow\frac{\mathrm{sin}\:\mathrm{8x}}{\mathrm{sin}\:\mathrm{4x}}\:=\:\frac{\mathrm{sin}\:\mathrm{5x}}{\mathrm{sin}\:\mathrm{3x}}\:;\:\frac{\mathrm{2sin}\:\mathrm{4x}.\mathrm{cos}\:\mathrm{4x}}{\mathrm{sin}\:\mathrm{4x}}\:=\:\frac{\mathrm{sin}\:\mathrm{5x}}{\mathrm{sin}\:\mathrm{3x}} \\ $$$$\Rightarrow\mathrm{2sin}\:\mathrm{3x}.\mathrm{cos}\:\mathrm{4x}\:=\:\mathrm{sin}\:\mathrm{5x} \\ $$$$\Rightarrow\mathrm{sin}\:\mathrm{7x}+\mathrm{sin}\:\left(−\mathrm{x}\right)=\mathrm{sin}\:\mathrm{5x} \\ $$$$\Rightarrow\mathrm{sin}\:\mathrm{7x}−\mathrm{sin}\:\mathrm{5x}\:+\mathrm{sin}\:\left(−\mathrm{x}\right)=\mathrm{0} \\…

Question-51245

Question Number 51245 by Tawa1 last updated on 25/Dec/18 Answered by afachri last updated on 25/Dec/18 $$\left(\mathrm{2}\right)\:\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{evaluate}}\:\bigtriangleup{H}_{\mathrm{Reaction}} \:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{bond}}\:\boldsymbol{\mathrm{energy}}\:: \\ $$$$\bigtriangleup{H}_{\mathrm{Reaction}} \:=\:\bigtriangleup{H}_{\mathrm{r}} \:−\:\bigtriangleup{H}_{\mathrm{p}} \\ $$$$\bigtriangleup{H}_{\mathrm{p}} \:;\:\left(\:\mathrm{N}−\mathrm{N}\right)\:+\:\mathrm{4}\left(\mathrm{N}−\mathrm{H}\right)\:=\:\left(+\mathrm{167}\right)\:\:+\:\:\mathrm{4}\left(\mathrm{385}.\mathrm{9}\right)…

Question-182311

Question Number 182311 by mnjuly1970 last updated on 07/Dec/22 Commented by Frix last updated on 07/Dec/22 $$\mathrm{Another}\:\mathrm{question}: \\ $$$$\mathrm{At}\:\mathrm{which}\:\mathrm{angle}\:\alpha\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangles} \\ $$$${ABY}\:\mathrm{and}\:{BCY}\:\mathrm{are}\:\mathrm{equal}? \\ $$ Commented by…

Question-182292

Question Number 182292 by HeferH last updated on 07/Dec/22 Answered by Acem last updated on 07/Dec/22 $$\:{x}=\:\cancel{\mathrm{90}°}\:\:\:\:“{I}\:{doupt}'' \\ $$$$\:{from}\:{the}\:{common}\:{side}\:{and}\:{the}\:\mathrm{2}\:{equals}\:{bases} \\ $$$$\:\frac{\mathrm{sin}\:\mathrm{40}}{\mathrm{sin}\:{x}}=\:\frac{\mathrm{sin}\:\mathrm{20}}{\mathrm{sin}\:\mathrm{120}−{x}}\:\:\Leftrightarrow\:\:\frac{\mathrm{2}\:\mathrm{cos}\:\mathrm{20}}{\mathrm{sin}\:{x}}=\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{120}−{x}} \\ $$$$\:\mathrm{2}\:\mathrm{cos}\:\mathrm{20}\:\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{cos}\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{sin}\:{x}\right)=\:\mathrm{sin}\:{x} \\ $$$$\:\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{20}\:\mathrm{cos}\:{x}=\:\mathrm{sin}\:{x}\:\left(\mathrm{1}−\:\mathrm{cos}\:\mathrm{20}\right)…