Answer:
25.5 feet
Explanation:
we are given the following:
initial angle of elevation = 19.6 degrees
final angle of elevation = 29.4 degrees
distance from the point of elevation = 123 feet
find the increase in height (rise) of the balloon ?
we should first take not that the hot air balloon, the point of elevation on the ground and the point directly under the passenger form a right angel triangle with:
- The distance between the hot air balloon and the point of elevation on the ground forming the hypotenuse
- The distance between the point of elevation and the point directly under the passenger forming the adjacent side
- The distance between the point directly under the passenger and the hot air balloon forming the opposite side
- The angle of elevation is the angle formed between the adjacent side and the hypotenuse ( the hot air balloon, the point of elevation and the point directly under the passenger)
- The increase in height would be the height at the final angle elevation minus the height at the initial angle of elevation.
This heights can be gotten from applying the phytaghoras theorem where
tan (angle of elevation) =\frac{height}{adjacent side}
height = adjacent side × tan (angle if elevation)
(adjacent side is the distance from the point of elevation = 123 feet while the angle of elevation = 19.6 degrees and 29.4 degrees )
- At the final angle of elevation
height = 123 x tan 29.4 = 69.3 feet
- At initial angle of elevation
height = 123 x tan 19.6 = 43.8 feet
increase in height =69.3 - 43.8 = 25.5 feet
