To find the angle of elevation at which Meekah is looking at the bird, we can use the sine, cosine, or tangent functions from trigonometry. We'll use the tangent function, which relates the angle of elevation to the opposite side (the height of the street light) and the adjacent side (the distance from the base of the street light).
Let \( h \) be the height of the street light, \( d = 8 \) feet be the distance from Meekah to the base of the street light, and the hypotenuse \( L = 16 \) feet be the line of sight to the top of the street light. We can first find the height \( h \) using the Pythagorean theorem:
\[ L^2 = h^2 + d^2 \]
Substituting in the values we know:
\[ 16^2 = h^2 + 8^2 \]
Calculating the squares:
\[ 256 = h^2 + 64 \]
Now, subtract 64 from both sides:
\[ 256 - 64 = h^2 \]
\[ 192 = h^2 \]
Taking the square root of both sides to find \( h \):
\[ h = \sqrt{192} \approx 13.856 \]
Next, we need to find the angle of elevation \( \theta \) using the tangent function:
\[ \tan(\theta) = \frac{h}{d} \]
Substituting in our values for \( h \) and \( d \):
\[ \tan(\theta) = \frac{13.856}{8} \]
Calculating the right side:
\[ \tan(\theta) \approx 1.732 \]
Now, to find \( \theta \), we take the arctangent (inverse tangent):
\[ \theta = \tan^{-1}(1.732) \]
Using a calculator:
\[ \theta \approx 60^\circ \]
Thus, the angle of elevation with which Meekah is looking at the bird, rounded to the nearest whole degree, is:
\[ \boxed{60} \]