Answer:
[tex]sin\ x = \frac{15}{17}[/tex]
Step-by-step explanation:
So in this case, it's similar to the previous question you asked, except this time you know cosine, and as you may know cosine is defined as: [tex]\frac{adjacent}{hypotenuse}[/tex] and sine is defined as: [tex]\frac{opposite}{hypotenuse}[/tex]. So all we need to solve for is the opposite side, but since we know two sides, we can solve for the other using the Pythagorean identity: [tex]a^2+b^2=c^2[/tex]
Plug in known values:
[tex]8^2 + b^2 = 17^2[/tex]
Simplify:
[tex]64 + b^2 = 289\\b^2 = 225\\b = 15[/tex]
So the opposite side is 15, and the hypotenuse is already given, in this case it's 17 (the denominator of cosine). So plugging this into the definition of sin gives you: [tex]\frac{15}{17}[/tex]
