Question

question 9
the path of a satellite orbiting the earth causes it to pass directly over two tracking stations a and b,
which are 52 km apart. when the satellite is on one side of the two stations, the angles of elevation at
a and b are measured to be 88.1° and 83.3°, respectively.
note: the picture is not drawn to scale.
how far is the satellite from station a?
distance from a = km
how high is the satellite above the ground?
height = km
enter your answer as a number; your answer should be accurate to 2 decimal places.
question help: video message instructor

Explanation:

Step1: Label triangle and find angles

Let satellite = S. In △SAB: AB=52 km, ∠SBA=83.3°, ∠SAB=180°-88.1°=91.9°, so ∠ASB=180-83.3-91.9=4.8°.

Step2: Apply Law of Sines for SA

Law of Sines: $\frac{SA}{\sin83.3°}=\frac{AB}{\sin4.8°}$
$SA=\frac{52×\sin83.3°}{\sin4.8°}$
$\sin83.3°≈0.993$, $\sin4.8°≈0.0837$
$SA≈\frac{52×0.993}{0.0837}≈619.57$ km.

Step3: Calculate height h

h = SA×sin88.1°
$\sin88.1°≈0.9995$
h≈619.57×0.9995≈619.26 km.

Answer:

distance from A = 619.57 km
height = 619.26 km