Answer: [tex]\frac{8}{17}[/tex] or 8:17
Step-by-step explanation:
For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-
[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]
Given: A right triangle with hypotenuse = 68 units
The side adjacent to S = 60
Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get
[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]
Thus, the side opposite to S = 32 units
Now, the trigonometric ratio for sin S is given by :-
[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]
Hence, the trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17
