To find the height of the bird (h) flying over the school, we can use trigonometry, specifically the tangent function. In a right triangle, the tangent of an angle is defined as the ratio of the opposite side (height of the bird, h) to the adjacent side (distance from the observer to the school, which is 500 feet in this case).
Given:
- Distance from observer to school (adjacent side) = 500 feet
- Angle of elevation (θ) = 39°
We can set up the following relationship using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Substituting in our known values:
\[ \tan(39^\circ) = \frac{h}{500} \]
To find h, we can rearrange this equation to solve for h:
\[ h = 500 \cdot \tan(39^\circ) \]
Now, we need to calculate \(\tan(39^\circ)\). Using a calculator:
\[ \tan(39^\circ) \approx 0.8098 \]
Now substitute this value back into the equation for h:
\[ h = 500 \cdot 0.8098 \]
Calculating this gives:
\[ h \approx 404.9 \text{ feet} \]
Thus, the height of the bird flying over the school is approximately 404.9 feet.
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