A rocket tracking station has two telescopes A and B placed 1.9 miles apart. The telescopes lock onto a rocket and transmit their anlges of elevation to a computer after a rocket launch. what is the distance to the rocket

1. Is the rocket launch-pad midway between the two telescopes?

2. What are the observed angles of elevation?

To determine the distance to the rocket, we need to use triangulation, which involves using the angles of elevation from the two telescopes and their separation distance. Here's how you can calculate it:

1. Let's say telescope A measures an angle of elevation of θA, and telescope B measures an angle of elevation of θB.

2. Draw a triangle with telescope A at one corner, telescope B at another corner, and the rocket at the third corner.

3. The distance between the telescopes, which is given as 1.9 miles, forms the baseline of the triangle.

4. The angles of elevation from the telescopes to the rocket represent the other two angles of the triangle.

5. Using trigonometry, we can calculate the distance to the rocket. We need to calculate the lengths of the two sides of the triangle adjacent to the angles of elevation.

6. Draw a line from telescope A to the rocket and label it as side A. Similarly, draw a line from telescope B to the rocket and label it as side B.

7. To find side A, we can use the following formula: side A = baseline (1.9 miles) * tan(θA).

8. To find side B, we can use the same formula: side B = baseline (1.9 miles) * tan(θB).

9. The distance to the rocket can then be calculated using the Pythagorean theorem: Distance to the rocket = √(side A^2 + side B^2).

By plugging in the values for θA and θB into the formulas above, you can calculate the distance to the rocket accurately.