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Question Number 14724 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 03/Jun/17

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 03/Jun/17

$A B = 13, B C = 16, A C = 15$ $A D = D C, D E ⊥ A C$ $. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .$ $D E = ?$
	Answered by mrW1 last updated on 04/Jun/17

	$\cos ∠ C = \frac{15^{2} + 16^{2} - 13^{2}}{2 \times 15 \times 16} = 0.65$ $\sin ∠ C = \sqrt{1 - 0 . 65^{2}} = 0.7599$ $D E = C D \times \tan ∠ C$ $= \frac{15}{2} \times \frac{0.7599}{0.65} = 8.768$
	Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 04/Jun/17

	$n i c e a n d s m a r t! t h a n k a l o t m y m a s t e r .$
	Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 04/Jun/17

	$c o s C = \frac{b^{2} + a^{2} - c^{2}}{2 a b}$ $s i n C = \frac{2 S}{a b}$ $t g C = \frac{\frac{2 S}{a b}}{\frac{a^{2} + b^{2} - c^{2}}{2 a b}} = \frac{4 S}{a^{2} + b^{2} - c^{2}}$ $D E = C D . t g C = \frac{b}{2} . \frac{4 S}{a^{2} + b^{2} - c^{2}} = \frac{2 b . S}{a^{2} + b^{2} - c^{2}}$ $D E = \frac{2 b . S}{2 a b . c o s C} = \frac{S}{a . c o s C} .$
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