The distances from the point the plane leaves the ground are given by the
trigonometric relationships of right triangle and Pythagoras theorem.
- A) The minimum distance to the base of the tower is approximately <u>874.57 ft</u>.
- B) The minimum distance to the top of the tower is approximately <u>882.76 ft</u>.
Reasons:
A) The angle with which the airplane climbs, θ = 11°
Height of the tower which the airplane flies, T = 120 foot
The clearance between the tower and the airplane, C = 50 feet
Required:
The minimum distance between the point where the plane leaves the ground and the base of the tower,
Solution:
Height at which the plane flies over the tower, h = T + C
Therefore, h = 120 ft. + 50 ft. = 170 ft.
At the point the plane leaves the ground, we have;
Which gives;
- The minimum distance between the point where the plane leaves the ground and the base of the tower,
≈ <u>874.57 ft</u>.
B) The minimum distance between the point where the plane leaves the ground and the tower, <em>R</em>, is given by Pythagoras's theorem as follows;
R² = ² + T²
Which gives;
R = √(*874.57 ft.)² + (120 ft.²)) ≈ 882.76 ft.
- The distance from the point where the airplane leaves the ground to the tower, R ≈ <u>882.76 ft</u>.
Learn more about Pythagoras theorem here: