Answer
0.9
Work Step by Step
$115^{\circ}$ is in between $90^{\circ}$ and $180^{\circ}$ and therefore it is in quadrant II. In the second quadrant, the value of $\sin\theta$ is positive.
$\sin 115^{\circ}=\sin(180^{\circ}-115^{\circ})=\sin65^{\circ}$
We know that the value of $\sin60=\frac{\sqrt 3}{2}\approx0.866$
We expect the value of $\sin 65^{\circ}$ to be a little greater than that of $\sin60^{\circ}$ and therefore 0.9 should be closest to $\sin 115^{\circ}$.
