Question Number 185521 by Mingma last updated on 23/Jan/23
Commented by mr W last updated on 06/Feb/23
$${other}\:{solution}\:{see}\:{Q}\mathrm{186594} \\ $$
Answered by mr W last updated on 23/Jan/23
$$\frac{{a}}{\mathrm{sin}\:\mathrm{30}}=\frac{{b}}{\mathrm{sin}\:\mathrm{70}}=\frac{{c}}{\mathrm{sin}\:\mathrm{80}} \\ $$$$\frac{\mathrm{sin}\:\alpha}{{c}}=\frac{\mathrm{sin}\:\mathrm{70}}{{a}+{b}} \\ $$$$\mathrm{sin}\:\alpha=\frac{\mathrm{sin}\:\mathrm{70}}{\frac{{a}}{{c}}+\frac{{b}}{{c}}}=\frac{\mathrm{sin}\:\mathrm{70}}{\frac{\mathrm{sin}\:\mathrm{30}}{\mathrm{sin}\:\mathrm{80}}+\frac{\mathrm{sin}\:\mathrm{70}}{\mathrm{sin}\:\mathrm{80}}}=\frac{\mathrm{sin}\:\mathrm{70}\:\mathrm{sin}\:\mathrm{80}}{\mathrm{sin}\:\mathrm{30}+\mathrm{sin}\:\mathrm{70}} \\ $$$$\Rightarrow\alpha=\mathrm{40}° \\ $$
Commented by Rupesh123 last updated on 23/Jan/23
How alpha equals 40 from the last step?
Commented by mr W last updated on 23/Jan/23
$${i}\:{just}\:{calculated}\:{the}\:{value}\:{with}\:{a} \\ $$$${calculator}. \\ $$