A pilot is flying over a straight highway He determines the

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be angle x = 27 degree and angle y = 53 degree, as shown in the figure. (Round your answers to two decimal places.) Find the distance of the plane from point A. mi Find the elevation of the plane mi The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B, which are 35 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 degree and 84.2 degree, respectively. (Round your answers to the nearest mile.). How far is the satellite from station A? mi How high is the satellite above the ground? mi

Solution

let h=distance satellite is above ground
let x=distance from point on ground directly below satellite to tracking stations on the ground
let s=distance satellite from station A
h/x=tan 87º
h/(35+x)=tan 84.2º

h=x tan87º

h=(35+x)tan 84.2º
..
xtan87º=(35+x)tan84.2º
19.08x=344.6+9.85x
x=37.33
h=37.33*tan87712.3 mi
sin 87º=h/s
s=h/sin 87713.3 mi
distance satellite is above ground712.3 mi
distance satellite from station A 713.3 mi