Question 1030252: The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B, which are 85 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?
Answer: _______mi
(b) How high is the satellite above the ground?
Answer: _______mi
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
The problem can be solved by
using a triangle to depict the
positions of the Tracking stations
and the satellite.
Tracking stations A and B are the
opposite ends of the base of the triangle.
The satellite is at C the apex of the triangle.
The angle at C is = 180 - (87 + 84.2)
The angle at C is 8.8 degrees.
Using Sine rule
AC = side b
BC = side a
AB = side c
To find distance between satellite
and Station A:-
b/SinB = c/SinC
b/Sin(84.2) = 85/Sin(8.8)
b = 85 x sin(84.2)/sin(8.8)
b = 552.76
b = 553 miles
This is how far the satellite is
from Station A.
Now, draw a line down from C to
the base of the triangle.
This represents the height of
the satellite above the ground.
Where the line from C touches
the base we name point Y
We now have a right angled
triangle CYA.
∠A = 87 degrees
∠Y = 90 degrees
AC now the hypotenuse = 553 miles.
Using Trigonometric ratios:-
Sin = Opposite/Hypotenuse
Sin(87) = Opposite/553
Opposite = Sin(87) x 553
Opposite = 552 miles
This is the height of the satellite
above the ground.
Sorry so long winded!
Hope this helps :-)
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