Question

BALLOON The angle of depression from a hot air balloon in the air to a person on the ground is 41°. If the person steps back 12 feet, the new angle of depression is 25°. If the person is 6 feet tall, how far off the ground is the hot air balloon?

Answer 1

Answer:

16.06 ft

Step-by-step explanation:

The figure is attached below.

In triangle ACB:

$tan(41)=\frac{x}{y} \\x=ytan(41)$

In triangle ADB:

$tan(25)=\frac{x}{y+10} \\(y+10)tan(41)=x$

Therefore equating both equations gives:

$ytan(41) = (y+10)tan(25)\\ytan(41) = ytan(25)+10tan(25)\\ytan(41)-ytan(25)=10tan(25)\\y(tan(41)-tan(25))=10tan(25)\\y=\frac{10tan(25)}{(tan(41)-tan(25)} =11.5715ft$

Therefore x = 11.5715*tan(41) = 10.06 ft

The distance of the jot air balloon to ground = 10.06 + 6 = 16.06 ft