To find the angle of elevation to the bird, we can use some basic trigonometry.
First, we determine the vertical height difference between your eyes and the bird. Since you are 6 feet tall and the bird is perched on a building that is 13 feet tall, the height difference is:
\[ \text{Height difference} = 13 \text{ feet} - 6 \text{ feet} = 7 \text{ feet} \]
Next, we know the diagonal distance from you to the bird is 26 feet. We can use the sine function to find the angle of elevation. The sine of the angle is defined as the opposite side (height difference) over the hypotenuse (diagonal distance):
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{26} \]
Now we take the inverse sine (also known as arcsine) to find the angle:
\[ \theta = \arcsin\left(\frac{7}{26}\right) \]
Calculating this, we find:
\[ \theta \approx \arcsin(0.2692) \approx 15.7^\circ \]
Rounding to the nearest whole degree, the angle of elevation is:
\[ \theta \approx 16^\circ \]
Thus, the angle of elevation you are using to look at the bird is approximately 16 degrees.
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