To find the missing angle in the right triangle, we can use the cosine function. In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
In this triangle:
- The hypotenuse (the slanted side) is 5.
- The adjacent side (the side next to the angle we want to find) is 4.
We can use the inverse cosine function (cosine inverse or \(\cos^{-1}\)) to find the angle. Let's denote the angle we want to find as \( \theta \).
The cosine of \( \theta \) is given by: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{5} \]
Now calculating the angle: \[ \theta = \cos^{-1}\left(\frac{4}{5}\right) \]
Now we can compute this using a calculator: \[ \theta \approx \cos^{-1}(0.8) \]
Calculating it: \[ \theta \approx 36.87^\circ \]
Rounding to the nearest whole degree: \[ \theta \approx 37^\circ \]
Thus, the missing angle rounded to the nearest whole degree is \( \boxed{37} \).
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