Question

A large airplane (plane A) flying at 26,000 feet sights a smaller plane (plane B) travelling at an altitude of 24,000 feet. The angle of depression is 40 degrees. What is the line of sight distance (x) between the two planes? Show or illustrate the condition of the problem. ​

Answer 1

Answer:

The line of sight distance is 1285.58 feet.

Step-by-step explanation:

The situation is illustrated in the figure attached.

From the figure we see that the altitude difference of the planes and the distance between them form a right triangle with one angle of 40° .

The line of sight between the two planes is the hypotenuse of the triangle.

The altitude difference of the planes is

$26,000ft -24,000ft = 2000 ft.$

Therefore, if we call $x$ the line of sight distance, from trigonometry we have

$sin (40^0) = \frac{2000ft}{x}$

$\boxed{ x = 1285.58ft}$

Therefore, the line of sight distance (x) is 1285.58 feet.