Question

Observers 2 miles apart from each other on the ground observe a flying ufo in the air above them. At a particular time, observer A sees the UFO at an angle of elevation of 42° and observer B sees it at an angle of elevation of 38°. How high above the ground is the UFO?

Answer 1

To find the height of the UFO, you can use trigonometry to solve for the opposite side of two right triangles formed by the observers' angles of elevation. By rearranging the equations and using a calculator, you can find that the height of the UFO is approximately 2.172 miles above the ground.

Step-by-step explanation:

To find the height of the UFO, we can use trigonometry.

Let's assume that the height of the UFO above the ground is h.

We can create two right triangles, one for each observer, with the height of the UFO as the opposite side, the distance between the observers as the adjacent side, and the angles of elevation as the angles.

For observer A:

tan(42°) = h / 2

For observer B:

tan(38°) = h / 2

By rearranging the equations, we can solve for h.

h = 2 * tan(42°) = 2 * tan(38°)

Using a calculator, we can find that tan(42°) ≈ 1.086 and tan(38°) ≈ 0.781.

Therefore, h = 2 * 1.086 ≈ 2.172 miles.