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 62 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 86.4° and 85.2°, 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 C. $\angle ACB = 180^\circ - 86.4^\circ - 85.2^\circ = 8.4^\circ$

Step2: Apply Law of Sines for AC

$\frac{AC}{\sin(85.2^\circ)} = \frac{AB}{\sin(8.4^\circ)}$, $AB=62$
$AC = \frac{62 \cdot \sin(85.2^\circ)}{\sin(8.4^\circ)}$
$\sin(85.2^\circ)\approx0.9965$, $\sin(8.4^\circ)\approx0.1461$
$AC\approx\frac{62 \cdot 0.9965}{0.1461}\approx422.53$

Step3: Calculate height h

$h = AC \cdot \sin(86.4^\circ)$
$\sin(86.4^\circ)\approx0.9989$
$h\approx422.53 \cdot 0.9989\approx421.97$

Answer:

distance from A = 422.53 mi
height = 421.97 mi