You are stationed at a radar base in Warner Robins, GA and you observe an unidentified flying object at an altitude of 2000 m flying towards your radar base at an angle of 20 degrees. How far away from the radar base is that plane (hypotenuse)?

Once you made your diagram, and let the hypotenuse equal to h, this becomes a basic case of solving

sin 20º = 2000/h for h

To find the distance from the radar base to the plane, we can use trigonometry. The given information tells us the altitude of the plane and the angle it makes with the radar base.

We can start by drawing a diagram to visualize the situation. Let's consider the radar base as the starting point, label it as point A. Now, draw a vertical line from point A to represent the altitude of the plane. Label the point where the line intersects the ground as point C. Next, draw a line segment connecting point A and point C, and let's label it as the adjacent side of the angle. Finally, draw a line segment from point C to the plane, and label it as the hypotenuse, or the distance we are trying to find.

Now that we have our diagram, we can use the trigonometric function tangent (tan) to solve for the hypotenuse. In this case, we have the opposite side (the altitude) and the adjacent side (the distance from the radar base to the point where the altitude intersects the ground).

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. So, we can set up the equation:

tan(angle) = opposite / adjacent

In this case, the angle is 20 degrees, the opposite side is the altitude (2000 m), and the adjacent side is the distance from the radar base to point C (which we want to find).

Plugging in the values, we have:

tan(20°) = 2000 m / adjacent

Now, to solve for the adjacent side (the distance we are trying to find), we rearrange the equation:

adjacent = 2000 m / tan(20°)

Using a calculator, we can find the value of tangent for 20 degrees, and then divide 2000 m by that value to get the distance from the radar base to the point where the altitude intersects the ground.

Once we have this distance, we can add it to the distance from point C to the plane (which is the altitude) to get the total distance from the radar base to the plane.