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Question Number 181221 by cortano1 last updated on 23/Nov/22

Answered by mr W last updated on 23/Nov/22

Commented by cortano1 last updated on 23/Nov/22

$$\mathrm{nicesolution}$$

Commented by mr W last updated on 23/Nov/22

$$\mathrm{\Delta }GEA\equiv \mathrm{\Delta }CED$$$$\Rightarrow \left[ABCD\right]=\left[\mathrm{\Delta }GBC\right]$$$$CB=34+8.5=42.5$$$$CG=2\times 16=32$$$$\cos \alpha =\frac{{16}^2+{34}^2-{30}^2}{2\times 16\times 34}=\frac{8}{17}$$$$\Rightarrow \sin \alpha =\sqrt{1-{\left(\frac{8}{17}\right)}^2}=\frac{15}{17}$$$$\left[\mathrm{\Delta }GBC\right]=\frac{CG\times CB\times \sin \alpha }{2}$$$$=\frac{32\times 42.5\times 15}{2\times 17}=600$$

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