A rezolva triunghiul inseamna sa aflam lungimile celor 3 laturi si masurile celor 3 unghiuri
a=BC=12 cm
b=AC=12 cm
∡C=105°
Daca AC=BC⇒ ΔABC isoscel⇒ ∡A=∡B
∡A=∡B=(180-105):2=75:2=37,5°=37°30'
Aplicam teorema lui Pitagora generalizata:
AB² = AC² +BC² - 2AC·BC cos(∡C)
Aflam cos 105° din formula:
cos(a+b)=cos a×cos b-sin a×sin b
cos(60+45)=cos60°×cos45°-sin60°×sin45°
[tex]cos(60+45)=\frac{1}{2}\cdot \frac{\sqrt{2} }{2}-\frac{\sqrt{3} }{2}\cdot \frac{\sqrt{2} }{2}=\frac{\sqrt{2}-\sqrt{6} }{4}[/tex]
[tex]AB^2=144+144-2\cdot144\cdot \frac{\sqrt{2} -\sqrt{6} }{4} \\\\AB^2=288-72(\sqrt{2}-\sqrt{6})\\\\ AB=\sqrt{288-72(\sqrt{2}-\sqrt{6})}[/tex]
Un alt exercitiu gasesti aici: https://brainly.ro/tema/84699
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