Question

You are at a parade looking up at a large balloon floating directly above the street. You are 60 ft from a point on the street directly beneath the balloon. 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. Estimate the height, h, of the balloon to the nearest foot. Answer with the only numeric value.

Answer 1

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 :

`h=d* tan\theta`

( Here ,
`\theta` is angle of elevation )

Now , distance of top of balloon from ground :

`H=60* tan53^o\\\\H=79.62\ ft`

Also , distance of bottom of balloon from ground :

`h=60* tan 29^o\\\\h=33.26\ ft`

Now , height of balloon is given by :

`H-h=79.62-33.26=46.36\ ft` .

Therefore , the height of the balloon to the nearest foot is 46.36 ft .

Hence, this is the required solution .