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Question Number 186549 by Mingma last updated on 05/Feb/23

Answered by mr W last updated on 06/Feb/23

$$sayAD=AC=CE=a$$$$AE=2a\cos 70°$$$${DE}^2=a^2+{\left(2a\cos 70\right)}^2-2a\times 2a\cos 70\times \cos 50$$$$2^2=a^2(1+4{\cos }^{2}70-4\cos 70\times \cos 50)$$$$a^2=\frac{4}{1+4{\cos }^{2}70-4\cos 70\times \cos 50}$$$$areaofADE:$$$$\left[ADE\right]=\frac{a\times 2a\cos 70\times \sin 50}{2}$$$$=a^2\cos 70\sin 50$$$$=\frac{4\cos 70\sin 50}{1+4{\cos }^{2}70-4\cos 70\times \cos 50}$$$$\approx 1.781$$

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