Question

calculeaza cos de A stiind ca sin de A=√3/2 si unghiul A este ascutit

Answer 1

Fie B unghiul drept si C celalalt unghi ascutit
$sinA=\frac{BC}{AC} \\ \\ \frac{BC}{AC}=\frac{\sqrt{3}}{2} \\ \\ 2\cdot BC=AC\sqrt{3} \\ \\ BC=\frac{AC\sqrt{3}}{2}$$AB^2=AC^2-BC^2 \\ \\ =AC^2-\Big(\frac{AC\sqrt{3}}{2}\Big)\Up^2 \\ \\ =AC^2-\frac{3\cdot AC^2}{4} \\ \\ =\frac{AC^2}{4} \\ \\ AB=\sqrt{\frac{AC^2}{4}}=\frac{AC}{2} \\ \\ cosA=\frac{AB}{AC}=\frac{\frac{AC}{2}}{AC}=\frac{AC}{2AC}=\frac{1}{2}$