Question

Trigonometry Problem, only solve if you know how and can tell me how to solve it.

Answer 1

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 874.57 ft.

• B) The minimum distance to the top of the tower is approximately 882.76 ft.

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, $\displaystyle d_{min}}$

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;

• $\displaystyle tan(\theta) = \mathbf{\frac{h}{d_{min}}}$

Which gives;

$\displaystyle tan(11^{\circ}) = \frac{170 \, ft.}{d_{min}}$

$\displaystyle d_{min} = \mathbf{\frac{170 \, ft.}{tan(11^{\circ})}} \approx 874.57 ft.$

• The minimum distance between the point where the plane leaves the ground and the base of the tower, $\displaystyle d_{min}}$ ≈ 874.57 ft.

B) The minimum distance between the point where the plane leaves the ground and the tower, R, is given by Pythagoras's theorem as follows;

R² = $\displaystyle \mathbf{d_{min}}}$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 ≈ 882.76 ft.

Learn more about Pythagoras theorem here:

brainly.com/question/11256912