+0  
 
0
294
1
avatar
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
Sort: 

1+0 Answers

 #1
avatar+3080 
0
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)
admin  Mar 7, 2012

9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details