Given :
Distance from where you can directly beneath the balloon , d = 60 ft .
To see the top of the balloon you look up at an angle of 53 degrees.
To see the bottom of the balloon you look up at an angle of 29 degrees.
To Find :
The height, h, of the balloon to the nearest foot.
Solution :
Height from ground is given by :
[tex]h=d\times tan\theta[/tex]
( Here , [tex]\theta[/tex] is angle of elevation )
Now , distance of top of balloon from ground :
[tex]H=60\times tan53^o\\\\H=79.62\ ft[/tex]
Also , distance of bottom of balloon from ground :
[tex]h=60\times tan 29^o\\\\h=33.26\ ft[/tex]
Now , height of balloon is given by :
[tex]H-h=79.62-33.26=46.36\ ft[/tex] .
Therefore , the height of the balloon to the nearest foot is 46.36 ft .
Hence, this is the required solution .
