To find the angle of elevation, we can use the cosine function in a right triangle. The cosine of an angle is defined as the ratio of the adjacent side (the distance from Meekah to the base of the street light) to the hypotenuse (the line of sight to the top of the street light).
Let:
- \( d \) = distance from Meekah to the base of the street light = 8 feet
- \( h \) = height of the street light (which we can find using the distance and the hypotenuse)
- \( L \) = line of sight = 16 feet
- \( \theta \) = angle of elevation
The cosine of the angle can be expressed as: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{d}{L} \] Substituting in the values we have: \[ \cos(\theta) = \frac{8}{16} = 0.5 \]
Now, we can find the angle \( \theta \) using the inverse cosine function: \[ \theta = \cos^{-1}(0.5) \]
Calculating this gives: \[ \theta = 60^\circ \]
Therefore, the angle of elevation with which Meekah is looking at the bird is approximately 60 degrees.
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