Question

Sinusul unui unghi ascutit al unui triunghi dreptunghic este $\frac{2}{3}$.Cosinusul unghiului respectiv este...

Answer 1

ΔABC, mas<A=90
sin<B= 2/3                  => cos <B= 1/2/3= 1* 3/2= 3/2

cos<B=3/2

Answer 2

Avem ΔABC dreptunghic in A  (<A = 90°)

sin <B = b/a  = 2/3
cos <B = c/a
Aplicam teorema lui Pitagora:
b² + c² = a²

$\frac{b^{2}+c^{2}}{a^{2}}=1<=> \frac{b^{2}}{a^{2}}+\frac{c^{2}}{a^{2}}=1 \\ \frac{c^{2}}{a^{2}}=1-\frac{b^{2}}{a^{2}}=> \frac{c}{a}= \sqrt{1-\frac{b^{2}}{a^{2}}}=\sqrt{1-\frac{2^{2}}{3^{2}}} = \\ = \sqrt{1-\frac{4}{9}}= \sqrt{ \frac{5}{9}}= \frac{ \sqrt{5} }{3}$

=>  cos <B = √5 / 3