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# pre-cal

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A hot air balloon is sighted at the same time by two friends who are 1.9 miles apart on the same side of the balloon. The angles of the elevation from the two friends are 12.5 degrees and 18 degrees. How high is the balloon? Round to the nearest decimal place.
Guest Mar 7, 2012
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baloon.png

d2=d1+1.9

tan( 18.5 ) = h/d1
tan( 12.5 ) = h/d2

tan( 18.5 )*d1 = h
tan( 12.5 )*d2 = h

tan( 18.5 )*d1=tan( 12.5 )*d2
tan( 18.5 )*d1=tan( 12.5 )*(d1+1.9)
tan( 18.5 )*d1=tan( 12.5 )*d1+tan( 12.5 )*1.9
tan( 18.5 )*d1-tan( 12.5 )*d1=tan( 12.5 )*1.9
d1*(tan( 18.5 )-tan( 12.5 ))=tan( 12.5 )*1.9
d1=(tan( 12.5 )*1.9)/(tan( 18.5 )-tan( 12.5 ))
[input](tan( 12.5 )*1.9)/(tan( 18.5 )-tan( 12.5 ))[/input]
d1= 3.73088935653542mi
h = tan( 18.5 )*d1
[input]tan( 18.5 )*3.73088935653542[/input]
h=1.24833811627684120894 (Balloon height)

test:
d2 = d1+1.9 = 5.63088935653542
h = tan( 12.5 )*d2= 1.24833811627684143082 (check)

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