i really need help!!!! please add the formula as well

Accepted Solution

Answer:[tex]Sin(\alpha)=\frac{2}{3}[/tex]Step-by-step explanation:We need a simple identity to solve for sine of an obtuse angle (angle greater than 90 degrees).We know,[tex]Sin(180-\alpha)=\alpha[/tex]So the value of [tex]Sin\alpha[/tex] would depend on the triangle we can make on the left side of the coordinate system shown.The triangle would be as shown in the attached figure.This triangle has base length of [tex]\sqrt{5}[/tex] and height of 2. The hypotenuse, r, can be solve using pythagorean theorem:[tex](\sqrt{5} )^2+(2)^2=r^2\\5+4=r^2\\9=r^2\\r=3[/tex]We know sin of an angle is "opposite" side over "hypotenuse". The triangle's opposite is "2" and hypotenuse is "3". So we can finally write:[tex]Sin(\alpha)=\frac{Opposite}{Hypotenuse}=\frac{2}{3}[/tex]