A weather balloon is sighted between points A and B which are 5 miles apart on level ground. The angle of elevation of the balloon from A is 37 degrees and it's angle of elevation from B is 58 degrees. Find the height, in feet, of the balloon above the ground.

Answer 1

tan 37 = h/x
tan 58 = h/(5-x)

x tan 37 = (5-x) tan 58
x (tan 37+tan 58) = 5 tan 58

x = 5 tan 58/ (tan 58 + tan 37)

then
h = x tan 37

Answer 2

ok.... so what is the answer?