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Question Number 177415 by HeferH last updated on 04/Oct/22

Answered by TheHoneyCat last updated on 04/Oct/22

This problem has no solution. If on the green (upper) triangle the notation “≠” means that it is isocelus (like usualy in geometry) than it CANNOT also be a rectangular triangle (except if you take b=0 but that would lead to an undefined fraction) If this notation is meaningless than you need an extra constraint on your problem (or to indicate a vatiable) If this notation means something else, you need to specity it cause I′ve never seen another use than “equal length” for it.

$$\mathrm{This}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}. \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{on}\:\mathrm{the}\:\mathrm{green}\:\left(\mathrm{upper}\right)\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{notation} \\ $$$$``\neq''\:\mathrm{means}\:\mathrm{that}\:\mathrm{it}\:\mathrm{is}\:\mathrm{isocelus}\:\left(\mathrm{like}\:\mathrm{usualy}\:\mathrm{in}\right. \\ $$$$\left.\mathrm{geometry}\right)\:\mathrm{than}\:\mathrm{it}\:\mathrm{CANNOT}\:\mathrm{also}\:\mathrm{be}\:\mathrm{a} \\ $$$$\mathrm{rectangular}\:\mathrm{triangle}\:\left(\mathrm{except}\:\mathrm{if}\:\mathrm{you}\:\mathrm{take}\:{b}=\mathrm{0}\right. \\ $$$$\left.\mathrm{but}\:\mathrm{that}\:\mathrm{would}\:\mathrm{lead}\:\mathrm{to}\:\mathrm{an}\:\mathrm{undefined}\:\mathrm{fraction}\right) \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{this}\:\mathrm{notation}\:\mathrm{is}\:\mathrm{meaningless}\:\mathrm{than}\:\mathrm{you}\:\mathrm{need} \\ $$$$\mathrm{an}\:\mathrm{extra}\:\mathrm{constraint}\:\mathrm{on}\:\mathrm{your}\:\mathrm{problem} \\ $$$$\left(\mathrm{or}\:\mathrm{to}\:\mathrm{indicate}\:\mathrm{a}\:\mathrm{vatiable}\right) \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{this}\:\mathrm{notation}\:\mathrm{means}\:\mathrm{something}\:\mathrm{else},\:\mathrm{you} \\ $$$$\mathrm{need}\:\mathrm{to}\:\mathrm{specity}\:\mathrm{it}\:\mathrm{cause}\:\mathrm{I}'\mathrm{ve}\:\mathrm{never}\:\mathrm{seen}\: \\ $$$$\mathrm{another}\:\mathrm{use}\:\mathrm{than}\:``{equal}\:{length}''\:\mathrm{for}\:\mathrm{it}. \\ $$

Commented by HeferH last updated on 04/Oct/22

Look carefully at the colors sir

$$\:{Look}\:{carefully}\:{at}\:\:{the}\:{colors}\:{sir} \\ $$

Answered by mr W last updated on 04/Oct/22

Commented by mr W last updated on 04/Oct/22

b=1×sin 75° (a/(sin 105°))=(1/(sin 45°)) ⇒a=((1×sin 75°)/(sin 45°)) (a/b)=((1×sin 75°)/(sin 45°×1×sin 75°))=(1/(sin 45°))=(√2)

$${b}=\mathrm{1}×\mathrm{sin}\:\mathrm{75}° \\ $$$$\frac{{a}}{\mathrm{sin}\:\mathrm{105}°}=\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{45}°}\:\Rightarrow{a}=\frac{\mathrm{1}×\mathrm{sin}\:\mathrm{75}°}{\mathrm{sin}\:\mathrm{45}°} \\ $$$$\frac{{a}}{{b}}=\frac{\mathrm{1}×\mathrm{sin}\:\mathrm{75}°}{\mathrm{sin}\:\mathrm{45}°×\mathrm{1}×\mathrm{sin}\:\mathrm{75}°}=\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{45}°}=\sqrt{\mathrm{2}} \\ $$

Commented by Tawa11 last updated on 04/Oct/22

Great sir.

$$\mathrm{Great}\:\mathrm{sir}. \\ $$

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