Question

3. A pilot is flying over a straight highway. He determines the angles of depressions to two mileposts that are 3.8 km apart, to be 58 and 30. Find the distance from the plane to point A.

Answer 1

2.1 km

Explanation:

Let's say the distance between the plane and the ground is y.

The horizontal distance between the plane and A is:

tan 58° = y / x₁

x₁ = y / tan 58°

x₁ = 0.625 y

The horizontal distance between the plane and B is:

tan 30° = y / x₂

x₂ = y / tan 30°

x₂ = 1.732 y

The difference between them is 3.8 km.

x₂ − x₁ = 3.8

1.732 y − 0.625 y = 3.8

1.107 y = 3.8

y = 3.432

The horizontal distance between the plane and point A is therefore:

x₁ = 0.625 × 3.432

x₁ = 2.145

Rounded, the plane is 2.1 km from point A.

Answer 2

4.05km

Explanation:

Because 58 represents the whole angle of where the airplane is, 58-30=28 degrees to find the small portion of the angle.

Let x represent the distance from the plane to point A.

3.8/sin(28) = x/sin(30) -> 3.8sin(30)/sin(28) = 4.05km