Question

Calculati lungimea laturii AC a triunghiului ABC, stiind ca BC = 8, A = pi / 4 si C = 7pi / 12.

(clasa a XII-a)

Teorema sinusurilor.. ? E urgent, va rog!

Answer 1

m(C) = π - (π/4 +7π/12) = π - 10π/12=(12π - 10π)/12 = 2π/12=π/6

T. sin ⇒ BC/sinA = AC/sinB  ⇒ AC =  BC·sinB/sinA ⇒

⇒ AC =( 8·1/2)/(√2/2) ⇒ AC = 4√2

Answer 2

fie a,b,c laturile ΔABC. a=8, A=180/4=45°, C=7x180/12=105°
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AC=b=?
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T.sin: a/sinA=b/sinB ⇒b=asinB  /  sinA = 8sin(180°-45°-105°)  /  sin45° =
= 8x sin30° : rad2 /2 = 8x1/2 x 2/rad2 =8/rad2 = 8/2rad2=4rad2=AC
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Succes in continuare!
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