Question

Fatoumata spots an airplane on radajy that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 6875 feet. Fatoumata initially measures an angle of elevation of 17∘ to the plane at point

A. At some later time, she measures an angle of elevation of 40∘ to the plane at point

Answer 1

The distance the plane traveled from point A to point B is approximately 22,651 feet, rounding to the nearest foot.

To find the distance the plane traveled from point A to point B, we can use trigonometry. Let x be the horizontal distance the plane traveled.

In △ABC, where A is the plane, B is point A, and C is point B:

- Angle ∠BAC is the initial angle of elevation, which is 17°.

- Angle ∠CAB is the final angle of elevation, which is 40°.

- Side BC is the constant altitude of the plane, which is 6875 feet.

Using the tangent function:

`\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \]`

`\[ \tan(17°) = (6875)/(x) \]`

Solving for x:

`\[ x = (6875)/(\tan(17°)) \]`

`\[ \text{distance traveled} = (6875)/(\tan(17^\circ)).\]`

Using a calculator:

`\[ \text{distance traveled} \approx (6875)/(0.3033) \approx 22,651 \text{ feet}.\]`

So, rounding to the nearest foot, the distance is approximately 22,651 feet.

Que. Fatoumata spots an airplane on radajy that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 6875 feet. Fatoumata initially measures an angle of elevation of 17∘ to the plane at point A. At some later time, she measures an angle of elevation of 40∘ to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.