Given the angle, θ is an angle in standard position
the terminal side passes through the point (5,12)
So,
[tex]\begin{gathered} x=5,y=12 \\ \\ \end{gathered}[/tex]
this means: opposite side = y = 12
Adjacent side = x = 5
We will find the hypotenuse (h) using the Pythagorean theorem
So,
[tex]\begin{gathered} h^2=x^2+y^2=5^2+12^2=25+144=169 \\ h=\sqrt[]{169}=13 \end{gathered}[/tex]
So,
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \\ \sin \theta=\frac{y}{h} \\ \sin \theta=\frac{12}{13} \end{gathered}[/tex]
So, the answer will be: 12/13
