Answer:
The ratio for sin(X) is [tex]\frac{\sqrt{119} }{12}[/tex]
The ratio for cos(X) is [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
- The ratio of the sine of a right triangle is:
[tex]sin(\alpha)=\frac{opposite-side}{hypotenuse}[/tex]
Since we need the ratio for angle X, [tex]\alpha =X[/tex]. From the picture we can infer that the opposite side of X is [tex]\sqrt{119}[/tex]. The hypotenuse (the side opposite to the right angle) is 12, so replacing the values:
[tex]sin(X)=\frac{\sqrt{119} }{12}[/tex]
- The ratio of the cosine is:
[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]
Similarly, [tex]\alpha =X[/tex], adjacent side = 5, and hypotenuse = 12, so
[tex]cos(X)=\frac{5}{12}[/tex]
