Question

The pilot of an airplane that is 300 meters above sea level spots two ships sailing due east of the plane's location. The angles of depression from the plane to the ships are 20° and 10°. How far apart are the ships? (Round the answer to the nearest meter)

Answer 1

To determine the distance between the two ships, we calculate the horizontal distances from the airplane to each ship using the tangent of the angles of depression and then subtract these distances.

Step-by-step explanation:

The problem involves using trigonometry to find the distance between two ships based on the angles of depression and the altitude of the airplane. Using the tangent of the angles of depression, we can find the horizontal distances to each ship from the airplane. Let's denote the horizontal distance to the first ship as D1 and to the second ship as D2.

To find D1, we use the angle of depression 20°:
tangent(20°) = altitude / D1. Therefore, D1 = altitude / tangent(20°).

For D2 with angle of depression 10°:
tangent(10°) = altitude / D2. Hence, D2 = altitude / tangent(10°).

Given the altitude is 300 meters, calculating these we get:
D1 ≈ 300 / tangent(20°)
D2 ≈ 300 / tangent(10°).

The distance between the ships is D2 - D1. After substituting the values and performing the calculations, we round the result to the nearest meter.