dererminer-la-valeur-x-

Question Number 183236 by a.lgnaoui last updated on 23/Dec/22

d e r e r m i n e r l a v a l e u r x ?

Commented by a.lgnaoui last updated on 23/Dec/22

Commented by mr W last updated on 24/Dec/22

“ p a r {m e s u r e}^{″} m e t h o d

x = 9

h o w i g o t ?

i m e a s u r e d w i t h a r u l e r .

Answered by mr W last updated on 24/Dec/22

s a y α = ∠ D C B

10 \tan α + 10 \sin α = 10

\Rightarrow \tan α + \sin α = 1

l e t t = \tan \frac{α}{2}

\Rightarrow \frac{2 t}{1 - t^{2}} + \frac{2 t}{1 + t^{2}} = 1

\Rightarrow t^{4} + 4 t - 1 = 0

\Rightarrow t = \frac{\sqrt{2 \sqrt{2} - 1} - 1}{\sqrt{2}}

\cos α = \frac{1 - t^{2}}{1 + t^{2}} = \frac{\sqrt{2} - 1 + \sqrt{2 \sqrt{2} - 1}}{2}

x = 10 \cos α = 5 (\sqrt{2} - 1 + \sqrt{2 \sqrt{2} - 1}) \approx 8.832

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