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
$${Top}\:{vertex}\:{of}\:{triangle}\: \\ $$$${Q}\left(\frac{{a}}{\mathrm{2}},\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}\right) \\ $$$${slope}\:{of}\:{line} \\ $$$$\frac{\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}}{\frac{{a}}{\mathrm{2}}−{x}}=\frac{\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}+{a}}{\frac{{a}}{\mathrm{2}}−{y}} \\ $$$$\Rightarrow\:\frac{{a}}{\mathrm{2}}−{y}=\frac{\mathrm{2}}{{a}\sqrt{\mathrm{3}}}\left(\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}+{a}\right)\left(\frac{{a}}{\mathrm{2}}−{x}\right) \\ $$$${y}=\frac{{a}}{\mathrm{2}}−\left(\mathrm{1}+\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}\right)\left(\frac{{a}}{\mathrm{2}}−{x}\right) \\ $$
Commented by TawaTawa last updated on 04/Nov/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$