Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

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.

$${i}\:{just}\:{calculated}\:{the}\:{value}\:{with}\:{a} \\ $$$${calculator}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com