Answer:
A)the satellite is at a distance of 1018.4 miles
B) the height of the satellite above the ground is 1017 miles.
Step-by-step explanation:
The diagram below shows the situation graphically so it's easier to understand.
To calculate this we need to use the tangent definition I.E. [tex]tan(\alpha ) = \frac{oposite side}{adyacent side}[/tex]
so for angle at point A it would be
tan(87) = h /x
for angle at pint B it would be tan
(84.2) = h / (x+50)
since h is the same for both we can pass terms and replace, then solve for x
tan(87)*x = h
tan (84.2)*(x+50) = h
∴
tan(87) * x = tan (84.2) * (x+50)
[tex]\frac{tan (87)}{tan (84.2)}[/tex] = [tex]\frac{x+50}{x}[/tex]
1.938 = 1 + [tex]\frac{50}{x}[/tex]
1.938 -1 = [tex]\frac{50}{x}[/tex]
x = [tex]\frac{50}{0.938}[/tex] = 53.3 mi
then using the tangent formula from before we can calculate h
tan(87) = h / 53.3
tan (87) / 53.3 = h
h = 1017 mi
then we can use the cos formula to calculate d
cos 87 = x / d
d = 53.3 / cos 87 = 1018.4 mi
