To find the angle θ using the inverse cosine, we can use the formula:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case, the bottom leg (56) can be considered as the adjacent side, and the hypotenuse is 65. Thus, we have:
\[ \cos(\theta) = \frac{56}{65} \]
Now, we can calculate the cosine value:
\[ \cos(\theta) = \frac{56}{65} \approx 0.8615 \]
Now we can find θ by taking the inverse cosine:
\[ \theta = \cos^{-1}(0.8615) \]
Calculating this using a calculator or a cosine inverse function:
\[ \theta \approx 30.5° \]
Therefore, the approximate measure of the missing angle θ is 30.5°.