Question

Sa se rezolve triunghiul ABC in care
a) a=12 b=12 c=105°

Answer 1

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°

$cos(60+45)=\frac{1}{2}\cdot \frac{\sqrt{2} }{2}-\frac{\sqrt{3} }{2}\cdot \frac{\sqrt{2} }{2}=\frac{\sqrt{2}-\sqrt{6} }{4}$

$AB^2=144+144-2\cdot144\cdot \frac{\sqrt{2} -\sqrt{6} }{4} \\\\AB^2=288-72(\sqrt{2}-\sqrt{6})\\\\ AB=\sqrt{288-72(\sqrt{2}-\sqrt{6})}$

Un alt exercitiu gasesti aici: https://brainly.ro/tema/84699

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