Answer:
[tex]\displaystyle \sin E=\frac{20}{101}[/tex]
Step-by-step explanation:
Recall that sine is the ratio between the opposite side and the hypotenuse in a right triangle:
[tex]\displaystyle \sin x=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
In the given triangle, with respect to E, the adjacent side is 99, and the hypotenuse is 101. So, we are not given the value of the opposite side.
Since it is a right triangle, we can use the Pythagorean Theorem. Hence:
[tex]OU^2+99^2=101^2[/tex]
Solving for OU (the opposite side) yields:
[tex]OU=\sqrt{101^2-99^2}=20[/tex]
Therefore, the opposite side is 20.
Hence:
[tex]\displaystyle \sin E=\frac{20}{101}[/tex]
