Question Number 77739 by ajfour last updated on 09/Jan/20
Commented by ajfour last updated on 09/Jan/20
$${Find}\:\:\:\frac{\mathrm{sin}\:\theta}{\mathrm{sin}\:\phi}\:\:{using}\:{a},{b},{c},\alpha. \\ $$
Commented by key of knowledge last updated on 09/Jan/20
$$\mathrm{not}\:\mathrm{have}\:\mathrm{add}\:\mathrm{informaion}? \\ $$
Answered by MJS last updated on 10/Jan/20
$$\mathrm{using}\:\mathrm{coordinate}\:\mathrm{method}\:\mathrm{I}\:\mathrm{get}\:\mathrm{these}: \\ $$$$\mathrm{horizontal}\:\mathrm{side}\:\mathrm{of}\:\mathrm{triangle} \\ $$$$\frac{\mathrm{2}\sqrt{\left({a}+{b}+{c}\right)\left({ab}+{ac}+\mathrm{4}{bc}\right){b}\left({b}+{c}\right){c}}}{{a}\left({b}+{c}\right)+{b}\left({b}+\mathrm{3}{c}\right)} \\ $$$$\mathrm{right}\:\mathrm{handed}\:\mathrm{side}\:\mathrm{of}\:\mathrm{triangle} \\ $$$$\frac{\left({a}+{b}\right)\left({a}\left({b}+{c}\right)+\left(\mathrm{3}{b}+{c}\right){c}\right)}{{a}\left({b}+{c}\right)+{b}\left({b}+\mathrm{3}{c}\right)}= \\ $$$$={a}+{b}+\frac{\left({a}+{b}\right)\left({c}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)}{{a}\left({b}+{c}\right)+{b}\left({b}+\mathrm{3}{c}\right)} \\ $$$$\mathrm{height}\:\mathrm{of}\:\mathrm{triangle} \\ $$$$\left({a}\left({b}+{c}\right)+\left(\mathrm{3}{b}+{c}\right){c}\right)\sqrt{\frac{{a}}{\left({ab}+{ac}+\mathrm{4}{bc}\right)\left({b}+{c}\right)}} \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{I}\:\mathrm{made}\:\mathrm{no}\:\mathrm{mistake}...\:\mathrm{please}\:\mathrm{draw}\:\mathrm{some} \\ $$$$\mathrm{examples}\:\mathrm{to}\:\mathrm{make}\:\mathrm{sure} \\ $$
Commented by ajfour last updated on 11/Jan/20
$${great}\:{sir},\:{thanks},\:{i}\:{shall}\:{check}.. \\ $$