SOLUTION: One observer estimates the angle of elevation to the basket of a hot air balloon to be 55�, while another observer 100 yards away estimates the angle of elevation to be 36�. How hi

Question 937463: One observer estimates the angle of elevation to the basket of a hot air balloon to be 55�, while another observer 100 yards away estimates the angle of elevation to be 36�. How high off the ground is the basket of the hot air balloon? Round to the nearest whole number.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
tan 55 = h/x
x= h/tan 55.................(1)
tan 36 = h/(100+x)
100tan 36 + x tan36 =h
x tan 36 =(h-100 tan 36)
x= (h-100 tan 36)/tan 36............(2)
equate (1) & (2)
(h-100 tan 36)/tan 36=h/tan 55
Simplify
h-100 tan 36 = h tan 36/tan 55
h- htan 36 /tan 55 = 100 tan 36
h-0.5h = 72.6
0.5h= 72.6
h = 145.3 feet

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