Question

the path of a satellite orbiting the earth causes it to pass directly over two tracking stations a and b, which are 43 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 87.2° and 83.3°, respectively. note: the picture is not drawn to scale. how far is the satellite from station a? distance from a = □ mi how high is the satellite above the ground? height = □ mi enter your answer as a number; your answer should be accurate to 2 decimal places. question help: video message instructor

Explanation:

Step1: Find angle at satellite

Let satellite be point S. In △SAB, ∠SAB=87.2°, ∠SBA=83.3°, so ∠ASB=180°−87.2°−83.3°=9.5°.

Step2: Apply Law of Sines for SA

Law of Sines: $\frac{SA}{\sin\angle SBA}=\frac{AB}{\sin\angle ASB}$.
$SA=\frac{AB \cdot \sin83.3°}{\sin9.5°}=\frac{43 \cdot \sin83.3°}{\sin9.5°}$.
Calculate: $\sin83.3°≈0.993$, $\sin9.5°≈0.165$, so $SA≈\frac{43×0.993}{0.165}≈259.53$.

Step3: Calculate height h

Height $h=SA \cdot \sin87.2°≈259.53×0.998≈259.01$.

Answer:

distance from A = 259.53 mi
height = 259.01 mi