Question

The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 35 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 are is the satellite from station A?
-Answer: 713 miles

B). How high is the satellite above the ground?
-Answer: _______

It says (on an example) for a similar problem B, that you can get

d=(1018.3mi)sin 87° = 1017 miles

and that's how you would get B. But the numbers don't add up for the example and the problem. I really need help :(

Extra note: the path from the satellite to the ground forms the edge of the triangle that forms the 90 turn at the bottom. When a line is drawn from the satellite to the the station next that line it has a 87° turn. But we are trying to figure out the How high is the satellite above the ground.

Answer 1

the height of the satellite and the line through the stations form the right angle of a right triangle

there are two hypotenuses (hypoteni?), one from each of the stations to the satellite

curious as to how you found A) without the height

h / a = tan(87º)

h / (a + 35) = tan(84.2º)

a tan(87º) = (a + 35) tan(84.2º)

a [tan(87º) - tan(84.2º)] =
35 tan(84.2º)

a = 37.3 mi ... this is the distance from A to the spot directly beneath the satellite

use trig to find all the other distances