Answer
$\dfrac{\sqrt{51}}{10}$
Work Step by Step
$\textbf{Step 1}$
We draw a right triangle with acute angle $\theta$ such that the leg adjacent $\theta$ has length $7$ and the hypotenuse has length $10$.
The length of $x$ (the leg opposite $\theta$) can be calculated using the Pythagorean theorem:
$$x=\sqrt{10^2-7^2}=\sqrt{51}.$$
$\textbf{Step 2}$
Calculate $\sin\theta$:
$$\sin\theta=\dfrac{opp}{hyp}=\dfrac{\sqrt{51}}{10}.$$
