Question Number 221944 by hardmath last updated on 13/Jun/25
Commented by hardmath last updated on 13/Jun/25
$$\mathrm{If}: \\ $$$$\bigtriangleup\mathrm{ABC}\:-\:\mathrm{Equilateral}\:\mathrm{Triangle} \\ $$$$\mathrm{MK}\:\parallel\:\mathrm{AB} \\ $$$$\mathrm{MN}\:\parallel\:\mathrm{AC} \\ $$$$\mathrm{ML}\:\bot\:\mathrm{AB} \\ $$$$\mathrm{AC}\:=\:\mathrm{a} \\ $$$$\mathrm{MN}\:=\:\mathrm{x} \\ $$$$\mathrm{MK}\:=\:\mathrm{y} \\ $$$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{ML}\:=\:\frac{\left(\mathrm{a}\:-\:\mathrm{x}\:-\:\mathrm{y}\right)\centerdot\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$
Answered by mr W last updated on 13/Jun/25
Commented by mr W last updated on 13/Jun/25
$${easy}\:{and}\:{clear}: \\ $$$${ML}={z}=\left({a}−{x}−{y}\right)\:\mathrm{sin}\:\mathrm{60}° \\ $$$$\:\:\:\:\:\:\:\:\:=\frac{\left({a}−{x}−{y}\right)\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$
Commented by hardmath last updated on 14/Jun/25
$$\mathrm{cool}\:\mathrm{thankyou}\:\mathrm{dear}\:\mathrm{professor} \\ $$