One angle is a right angle. The lengths of the sides adjacent to the right angle

Choice C is correct. The Pythagorean theorem states that for a right triangle, $a^2+b^2=c^2$, where $a$ and $b$ represent the lengths of the legs of the triangle and $c$ represents the length of its hypotenuse. In the triangle shown, the legs have lengths of $3$ and $7$. Substituting $3$ for $a$ and $7$ for $b$ in the equation $a^2+b^2=c^2$ yields $3^2+7^2=c^2$, which is equivalent to $9+49=c^2$, or $58=c^2$. Taking the positive square root of both sides of this equation yields $\sqrt{58}=c$. Thus, the value of $c$ is approximately $7.6$. Therefore, of the given choices, $7.6$ is the closest to the length of the triangle's hypotenuse.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.