To find the angle \( \theta \) using the inverse tangent ratio, we can use the tangent function definition in a right triangle. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In your case, it seems that you have:
- The length of the opposite side (9)
- The length of the adjacent side (13)
Using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{13} \]
To find the angle \( \theta \), we take the inverse tangent (also known as arctangent):
\[ \theta = \tan^{-1}\left(\frac{9}{13}\right) \]
Now we can calculate it. Using a calculator:
\[ \theta \approx \tan^{-1}(0.6923) \approx 39.39^\circ \]
Rounding to the nearest whole degree:
\[ \theta \approx 39^\circ \]
So, the missing angle \( \theta \) is approximately \( 39^\circ \).