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Question Number 193069 by Mingma last updated on 03/Jun/23

Answered by ajfour last updated on 03/Jun/23

Commented by ajfour last updated on 03/Jun/23

$$a=17\cos \theta$$$$p\sin \theta +10\sin \theta +6\cos \theta =a=17\cos \theta$$$$\Rightarrow p+10=11\cot \theta$$$$\cot \theta =\frac{6+p}{10}$$$$\Rightarrow 10\cos \theta -6+10=11\cot \theta$$$$10\cos \theta \sin \theta +4\sin \theta =11\cos \theta$$$$(1-t^2){(10t+4)}^2=121t^2$$$$t=\cos \theta \approx 0.76483$$$$a^2=289t^2\approx 169.05squnits$$

Commented by MM42 last updated on 04/Jun/23

$$itwasabeautifulsolution.$$$$p+10=11cot\theta$$$$p+6=10cot\theta$$$$\Rightarrow cot\theta =4\Rightarrow cos\theta =\frac{4}{\sqrt{17}}\Rightarrow a=\frac{20}{\sqrt{17}}\Rightarrow s=\frac{400}{17}$$$$$$

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