trigonometria

COS(β) = 4/5

SIN(β) = √(1 - (4/5)^2)

SIN(β) = 3/5

TAN(β) = SIN(β)/COS(β)

TAN(β) = 3/5/(4/5)

TAN(β) = 3/4

ΑC = ΑΒ·TAN(β)

ΑC = 8·(3/4) = 6

SIN(γ) = SIN(pi/2 - β)

SIN(γ) = COS(β) = 4/5

TAN(γ) = COT(β) = 4/3

2° terna pitagorica 6,8,10 

cos β = 4/5 = 0,8

sin β = 3/5 = 0,6 

AC = 6

BC = 10 

tan ϒ = AB/AC = 8/6 = 4/3 

sen^2 β + cos^2 β = 1;

cos β = 4/5;

sen^2 β  = 1 - cos^2 β;

sen β = radicequadrata( 1 - 16/25) = radice[(25 - 16)/25];

sen β = radice(9/25) = 3/5;

tan β  = senβ /cosβ  = 3/5 : 4/5 ;

tanβ  = 3/5 * 5/4 = 3/4;

tanβ  = AC / AB;  (cateto opposto fratto cateto adiacente a β );

cateto AC:

AC = AB * tanβ ;

AC = 8 * 3/4 = 6; (cateto opposto a β );

γ = angolo complementare a  β;

tan γ = AB / AC;

tan γ= 8/6 = 4/3.

ipotenusa BC = 10. (Terna pitagorica, 6; 8; 10 formano un triangolo rettangolo).

Ciao @saraaaaaaaaaaaaaaaaaaa

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$\small Cateto\,\overline{AC}= \overline{AB}×\tan\left[\cos^{-1}\left(\cos(\beta)\right)\right]$

$\small Cateto\,\overline{AC}= 8×\tan\left[\cos^{-1}\left(\dfrac{4}{5}\right)\right]$

$\small Cateto\,\overline{AC}= \cancel8^2×\dfrac{3}{\cancel4_1}= 2×3 = 6$

$\small \tan(\gamma)= \tan\left[180°-90°-\cos^{-1}\left(\cos(\beta)\right)\right]$

$\small \tan(\gamma)= \tan\left[90°-\cos^{-1}\left(\dfrac{4}{5}\right)\right]$

$\small \tan(\gamma)= \dfrac{4}{3}$