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Question Number 154085 by iloveisrael last updated on 14/Sep/21

Commented by iloveisrael last updated on 14/Sep/21

$f i n d a r e a o f t r i a n g l e A B C$
	Answered by EDWIN88 last updated on 14/Sep/21

	$l e t t = a l t i t u d e o f △ A B C$ $\Rightarrow \arctan (\frac{4}{t}) + \arctan (\frac{2}{t}) = \frac{π}{5}$ $\Rightarrow \frac{(\frac{6}{t})}{1 - \frac{8}{t^{2}}} = \tan \frac{π}{5} \approx 0.73$ $\Rightarrow \frac{6 t}{t^{2} - 8} = 0.73$ $\Rightarrow 0.73 t^{2} - 6 t - 5.84 = 0$ $\Rightarrow t = \frac{6 + \sqrt{36 + 17.05}}{1.46} \approx 9.1$ $a r e a o f △ A B C = \frac{1}{2} \times 6 \times 9.1 = 27.3$
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