+0  
 
0
356
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
 #1
avatar+3076 
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

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.