Question

In tiunghiul ABC unghiul A= 90 grade, unghiul B= 60 grade, iar CA=10 cm Aflati celelalte doua laturi.

Answer 1

Bună!

Δ₉₀°ABC: m(∡ABC)=60° ⇒ m(∡ACB)=30°

Metoda 1

sinB=$\frac{AC}{BC}$ ⇔ $\frac{\sqrt{3} }{2} =\frac{10}{BC} => BC=^{\sqrt{3} )} \frac{2*10}{\sqrt{3} } => BC=\frac{20\sqrt{3} }{3}$

T∡30°⇒ $AB=\frac{BC}{2}$ ⇒ $AB=\frac{20\sqrt{3} }{3} *\frac{1}{2} =\frac{10\sqrt{3} }{3}$

Metoda 2

notăm: BC=x , AB=$\frac{x}{2}$

T.P⇒ $10^{2} +(\frac{x}{2} )^{2} =x^{2} <=> 100+\frac{x^{2} }{4} =x^{2}/*4 <=> 400+x^{2} =4x^{2} <=> x^{2} - 4x^{2}=-400 <=> -3x^{2} =-400 => x^{2} =\frac{400}{3} => x= +-\sqrt{\frac{400}{3} } => x=+-\frac{20\sqrt{3} }{3} => x=\frac{20\sqrt{3} }{3}$

→ Laturile pot lua doar valori pozitive

AB=$\frac{x}{2} = \frac{20\sqrt{3} }{3} *\frac{1}{2} =\frac{10\sqrt{3} }{3}$