To find the angle formed between the top of the building and the shadow, we can use the relationship defined by the sine function in a right triangle.
We are given:
- The opposite side (the height of the building) is the vertical distance we've yet to calculate.
- The adjacent side (the shadow) measures 13 feet.
- The hypotenuse (the diagonal distance from the top of the building to the end of the shadow) measures 15 feet.
We will use the cosine function instead because we know the adjacent side and the hypotenuse: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Substituting the given values: \[ \cos(\theta) = \frac{13}{15} \]
Now we will calculate \(\theta\): \[ \theta = \cos^{-1}\left(\frac{13}{15}\right) \]
Calculating \(\cos^{-1}\left(\frac{13}{15}\right)\): Using a calculator, \[ \theta \approx 43.6° \text{ (approximately)} \]
Since this is close to 45°, you can round it for the available options given. However, to stay within the options provided, the most appropriate choice would be approximately 45°.
So the answer is approximately: 45°