# Math

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?

B). How high is the satellite above the ground?

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.

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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

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