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Question Number 201808 by ahmetgg last updated on 12/Dec/23

Commented by ahmetgg last updated on 12/Dec/23

Syhthetic solution please.

Answered by mr W last updated on 12/Dec/23

Commented by mr W last updated on 12/Dec/23

b=(a/(tan 17°)) c=b tan 47°=((a tan 47°)/(tan 17°)) d=(a/(tan 51°)) tan α=(c/d)=((a tan 47°)/(tan 17°×(a/(tan 51°))))=((tan 47° tan 51°)/(tan 17°)) ⇒α=tan^(−1) (((tan 47° tan 51°)/(tan 17°)))=77°

$${b}=\frac{{a}}{\mathrm{tan}\:\mathrm{17}°} \\ $$$${c}={b}\:\mathrm{tan}\:\mathrm{47}°=\frac{{a}\:\mathrm{tan}\:\mathrm{47}°}{\mathrm{tan}\:\mathrm{17}°} \\ $$$${d}=\frac{{a}}{\mathrm{tan}\:\mathrm{51}°} \\ $$$$\mathrm{tan}\:\alpha=\frac{{c}}{{d}}=\frac{{a}\:\mathrm{tan}\:\mathrm{47}°}{\mathrm{tan}\:\mathrm{17}°×\frac{{a}}{\mathrm{tan}\:\mathrm{51}°}}=\frac{\mathrm{tan}\:\mathrm{47}°\:\mathrm{tan}\:\mathrm{51}°}{\mathrm{tan}\:\mathrm{17}°} \\ $$$$\Rightarrow\alpha=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\:\mathrm{47}°\:\mathrm{tan}\:\mathrm{51}°}{\mathrm{tan}\:\mathrm{17}°}\right)=\mathrm{77}° \\ $$

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