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Question Number 180858 by Mastermind last updated on 18/Nov/22

Answered by mr W last updated on 18/Nov/22

$$A=2\times \frac{a\times a\times \tan \left[\frac{1}{2}(\frac{\pi }{2}-\alpha )\right]}{2}$$$$=a^2\tan (\frac{\pi }{4}-\frac{\alpha }{2})$$

Commented by Mastermind last updated on 18/Nov/22

$$\mathrm{With}\mathrm{full}\mathrm{details}\mathrm{explanation}\mathrm{boss}$$

Commented by mr W last updated on 18/Nov/22

Commented by mr W last updated on 18/Nov/22

$$2\beta +\alpha =\frac{\pi }{2}$$$$\Rightarrow \alpha =\frac{\pi }{4}-\frac{\alpha }{2}$$$$b=a\tan \alpha =a\tan (\frac{\pi }{4}-\frac{\alpha }{2})$$$$\frac{A}{2}=\frac{ab}{2}=\frac{a\times a\tan (\frac{\pi }{4}-\frac{\alpha }{2})}{2}$$$$\Rightarrow A=a^2\tan (\frac{\pi }{4}-\frac{\alpha }{2})$$

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