1. **State the problem:** Autumn spots a plane flying at a constant altitude of 69506950 feet. She measures the angle of elevation to the plane as 15° at point A and later as 38° at point B. We need to find the distance the plane traveled from A to B. 2. **Set up the scenario:** The plane is flying horizontally at altitude $h = 69506950$ feet. At points A and B on the ground, the angles of elevation to the plane are $\theta_A = 15^\circ$ and $\theta_B = 38^\circ$ respectively. 3. **Relate angles to horizontal distances:** Let $x_A$ and $x_B$ be the horizontal distances from points A and B to the point on the ground directly below the plane (the point where the plane will fly overhead). Using the tangent of the angle of elevation, $$\tan(\theta) = \frac{\text{altitude}}{\text{horizontal distance}}$$ So, $$x_A = \frac{h}{\tan(15^\circ)}$$ $$x_B = \frac{h}{\tan(38^\circ)}$$ 4. **Calculate $x_A$ and $x_B$:** $$x_A = \frac{69506950}{\tan(15^\circ)}$$ $$x_B = \frac{69506950}{\tan(38^\circ)}$$ Using approximate values: $\tan(15^\circ) \approx 0.2679$ $\tan(38^\circ) \approx 0.7813$ So, $$x_A \approx \frac{69506950}{0.2679} \approx 259423091.3$$ $$x_B \approx \frac{69506950}{0.7813} \approx 88934422.3$$ 5. **Find the distance traveled:** The plane travels from point A to point B, so the distance is $$d = x_A - x_B = 259423091.3 - 88934422.3 = 170488669.0$$ 6. **Final answer:** The plane traveled approximately $170488669.0$ feet from point A to point B.