Question

A plane is flying 1200 ft above the ground and spots a bird flying above. If the horizontal distance between the plane and the bird is 2000 ft and the angle of elevation is 71*, find the bird’s altitude.

Answer 1

We can use trigonometry to solve this problem.

Let's call the bird's altitude h. Then we can set up a right triangle with the following information:

- The height of the plane is 1200 ft.
- The horizontal distance between the plane and the bird is 2000 ft.
- The angle of elevation from the plane to the bird is 71°.

The opposite side of the triangle is h (the bird's altitude), the adjacent side is 2000 ft (the horizontal distance), and the hypotenuse is the distance from the plane to the bird (which we can find using trigonometry).

We can use the tangent function to find the hypotenuse:

tan(71°) = h/2000

h = 2000 tan(71°)

h ≈ 5945.5

So the bird's altitude is approximately 5945.5 ft.