Questions: QUESTION 8 An airplane rises at an angle of 11 degrees with the ground. Find the distance it has flown when it has covered a horizontal distance of 4500 feet.

Solution Steps

To find the distance the airplane has flown, we can use trigonometry. Specifically, we can use the cosine of the angle of elevation. The horizontal distance is the adjacent side of the right triangle, and the distance flown is the hypotenuse. We can use the cosine function to solve for the hypotenuse.

We are given:

• The angle of elevation, \(\theta = 11^\circ\)
• The horizontal distance covered, \(d_{\text{horizontal}} = 4500\) feet

To use trigonometric functions, we need to convert the angle from degrees to radians: \[ \theta_{\text{radians}} = \theta \times \left(\frac{\pi}{180}\right) \] \[ \theta_{\text{radians}} = 11 \times \left(\frac{\pi}{180}\right) \approx 0.1920 \]

The horizontal distance is the adjacent side of the right triangle, and the distance flown is the hypotenuse. Using the cosine function: \[ \cos(\theta) = \frac{d_{\text{horizontal}}}{d_{\text{flown}}} \] Solving for \(d_{\text{flown}}\): \[ d_{\text{flown}} = \frac{d_{\text{horizontal}}}{\cos(\theta)} \] \[ d_{\text{flown}} = \frac{4500}{\cos(0.1920)} \approx 4584.23 \text{ feet} \]

Final Answer