To find the measure of angle $\theta$, we will use trigonometry and the given triangle dimensions. Specifically, the triangle provides the opposite side ($10$) and the hypotenuse ($14$) relative to $\theta$.

The sine function relates the opposite side and hypotenuse: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10}{14}.$

First, calculate the sine value: $\sin(\theta) = \frac{10}{14} = 0.7143.$

Now, use the inverse sine function ($\sin^{-1}$) to find $\theta$: $\theta = \sin^{-1}(0.7143).$

Using a calculator: $\theta \approx 45.6^\circ.$

Final Answer:

The measure of $\theta$, to the nearest tenth of a degree, is: [ \boxed{45.6^\