Answer:
[tex]\frac{\sqrt{17} }{7}[/tex]
Step-by-step explanation:
Given
cosΘ = [tex]\frac{4\sqrt{2} }{7}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]
Then the hypotenuse of the right triangle is 7 and the adjacent side is 4[tex]\sqrt{2}[/tex]
To find the opposite side use Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
opp² + (4[tex]\sqrt{2}[/tex] )² = 7²
opp² + 32 = 49 ( subtract 32 from both sides )
opp² = 17 ( take the square root of both sides )
opp = [tex]\sqrt{17}[/tex]
Hence
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{17} }{7}[/tex]
