Tracking a satellite the path of a satellite orbiting the earth causes it to pass directly over two tracking stations a and b, which are 50 mi apart. when the satellite is on one side of the two stations, the angles of elevation at a and b are mea- sured to be 87. and 84. respectively.
(a) how far is the satellite from station a?
(b) how high is the satellite above the ground?

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.

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)

=

1.938 = 1 +

1.938 -1 =

x = = 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

the solution is 12x-6y