The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B, which are 95 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 87.0° and 84.2°, respectively. (Round your answers to the nearest mile.)

(a) How far is the satellite from station A?

_____mi

(b) How high is the satellite above the ground?

_____mi

1 answer

Draw a diagram. If the height is h,

h cot84° - h cot87° = 95

(a) the distance d is found via

h^2+(h cot87°)^2 = d^2