he path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B,

Question

The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B, which are 45 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87.0° and 84.2°, respectively. (Round your answers to the nearest mile.)

(a) How far is the satellite from station A?

___mi

(b) How high is the satellite above the ground?

 _____mi

Answer 1

In the previous submission, x gives the horizontal distance from A to the point on earth directly to the satellite. But what if the distance requested is the distance directly from A to the satellite?

.C ( the satellite)

B.......................A

Let b be the distance from A to C. We want to find b. Two ways to do this:

1) h^2 + x^2 = b^2. Use the h and x you found by the previous method submitted to find b.

2) First use the information in the problem to find the measures of the angles of triangle ABC.

Then use the the law of sines to find b.

Answer 2

Draw and label the distance from the satellite to the ground, h

Label the distance from A the line h, x

tan 84.2 = h / (x + 45)

tan 87 = h / x

Solve each for x.

Set the two equations equal and solve for h.