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Question Number 72871 by TawaTawa last updated on 04/Nov/19

Answered by ajfour last updated on 04/Nov/19

Commented by ajfour last updated on 04/Nov/19

Top vertex of triangle Q((a/2),((a(√3))/2)) slope of line (((a(√3))/2)/((a/2)−x))=((((a(√3))/2)+a)/((a/2)−y)) ⇒ (a/2)−y=(2/(a(√3)))(((a(√3))/2)+a)((a/2)−x) y=(a/2)−(1+(2/(√3)))((a/2)−x)

$${Top}\:{vertex}\:{of}\:{triangle}\: \\ $$$${Q}\left(\frac{{a}}{\mathrm{2}},\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}\right) \\ $$$${slope}\:{of}\:{line} \\ $$$$\frac{\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}}{\frac{{a}}{\mathrm{2}}−{x}}=\frac{\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}+{a}}{\frac{{a}}{\mathrm{2}}−{y}} \\ $$$$\Rightarrow\:\frac{{a}}{\mathrm{2}}−{y}=\frac{\mathrm{2}}{{a}\sqrt{\mathrm{3}}}\left(\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}+{a}\right)\left(\frac{{a}}{\mathrm{2}}−{x}\right) \\ $$$${y}=\frac{{a}}{\mathrm{2}}−\left(\mathrm{1}+\frac{\mathrm{2}}{\sqrt{\mathrm{3}}}\right)\left(\frac{{a}}{\mathrm{2}}−{x}\right) \\ $$

Commented by TawaTawa last updated on 04/Nov/19

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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