Math  /  Trigonometry

QuestionGlide Path A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are 17.517.5^{\circ} and 18.818.8^{\circ}. (a) Draw a diagram that visually represents the problem. (b) Find the air distance the plane must travel until touching down on the near end of the runway. (c) Find the ground distance the plane must travel until touching down. (d) Find the altitude of the plane when the pilot begins the descent.

Studdy Solution
Determine the altitude of the plane: - Use the tangent function for the angle of depression to the far end of the runway 18.8 18.8^\circ : tan(18.8)=altitudex+9000 \tan(18.8^\circ) = \frac{\text{altitude}}{x + 9000} . - Solve for the altitude: altitude=(x+9000)tan(18.8) \text{altitude} = (x + 9000) \cdot \tan(18.8^\circ) .
Solution: - The air distance PA PA and ground distance x x can be calculated using the altitude found in Step 4. - The altitude of the plane when the pilot begins the descent is calculated in Step 4.

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