Find the value of $\sin \theta$, given that $\tan \theta=1.771$, if $\theta$ is an acute angle. \[ \sin \theta= \] (Round to four decimal places as needed.)

Step 1 ：Given that $\tan \theta = 1.771$, we need to find the value of $\sin \theta$. We know that $\tan \theta = \frac{\sin \theta}{\cos \theta}$.

Step 2 ：Since $\theta$ is an acute angle, both $\sin \theta$ and $\cos \theta$ are positive. We can use the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$ to find the value of $\sin \theta$.

Step 3 ：First, let's find the value of $\cos \theta$ using the given value of $\tan \theta$: $\cos \theta = \frac{\sin \theta}{\tan \theta} = \frac{\sin \theta}{1.771}$.

Step 4 ：Now, we can substitute this expression for $\cos \theta$ into the Pythagorean identity: $\sin^2 \theta + \left(\frac{\sin \theta}{1.771}\right)^2 = 1$.

Step 5 ：Solving this equation for $\sin \theta$, we get two solutions: $\sin \theta \approx -0.8708$ and $\sin \theta \approx 0.8708$.

Step 6 ：Since $\theta$ is an acute angle, we know that $\sin \theta$ must be positive. Therefore, we can choose the positive solution.

Step 7 ：\(\boxed{\sin \theta \approx 0.8708}\) (rounded to four decimal places).