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Question-185521




Question Number 185521 by Mingma last updated on 23/Jan/23
Commented by mr W last updated on 06/Feb/23
other solution see Q186594
$${other}\:{solution}\:{see}\:{Q}\mathrm{186594} \\ $$
Answered by mr W last updated on 23/Jan/23
(a/(sin 30))=(b/(sin 70))=(c/(sin 80))  ((sin α)/c)=((sin 70)/(a+b))  sin α=((sin 70)/((a/c)+(b/c)))=((sin 70)/(((sin 30)/(sin 80))+((sin 70)/(sin 80))))=((sin 70 sin 80)/(sin 30+sin 70))  ⇒α=40°
$$\frac{{a}}{\mathrm{sin}\:\mathrm{30}}=\frac{{b}}{\mathrm{sin}\:\mathrm{70}}=\frac{{c}}{\mathrm{sin}\:\mathrm{80}} \\ $$$$\frac{\mathrm{sin}\:\alpha}{{c}}=\frac{\mathrm{sin}\:\mathrm{70}}{{a}+{b}} \\ $$$$\mathrm{sin}\:\alpha=\frac{\mathrm{sin}\:\mathrm{70}}{\frac{{a}}{{c}}+\frac{{b}}{{c}}}=\frac{\mathrm{sin}\:\mathrm{70}}{\frac{\mathrm{sin}\:\mathrm{30}}{\mathrm{sin}\:\mathrm{80}}+\frac{\mathrm{sin}\:\mathrm{70}}{\mathrm{sin}\:\mathrm{80}}}=\frac{\mathrm{sin}\:\mathrm{70}\:\mathrm{sin}\:\mathrm{80}}{\mathrm{sin}\:\mathrm{30}+\mathrm{sin}\:\mathrm{70}} \\ $$$$\Rightarrow\alpha=\mathrm{40}° \\ $$
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.
$${i}\:{just}\:{calculated}\:{the}\:{value}\:{with}\:{a} \\ $$$${calculator}. \\ $$

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