To find the angle of elevation from your eyes to the bird, we can use the inverse sine function (arcsin).
First, we need to find the height difference between the bird and your eyes. Since you are 5.5 feet tall and the bird is perched 23 feet up, the height difference is:
\[ \text{Height of the bird} - \text{Your height} = 23, \text{feet} - 5.5, \text{feet} = 17.5, \text{feet} \]
Next, we can use the relationship in a right triangle to find the angle of elevation. The height difference is the opposite side, and the diagonal distance (the hypotenuse) is 28 feet. The sine of the angle \(\theta\) can be expressed as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{17.5, \text{feet}}{28, \text{feet}} \]
Calculating that gives:
\[ \sin(\theta) = \frac{17.5}{28} \approx 0.625 \]
Now, we can find \(\theta\) using the inverse sine function:
\[ \theta = \arcsin(0.625) \]
Using a calculator:
\[ \theta \approx 38.68, \text{degrees} \]
Rounding it, the angle of elevation is approximately \(39^\circ\).
Therefore, the answer is:
39°