Question

While taking a ride in a hot-air balloon in Napa Valley, Francisco wonders how high he is. To find out, he chooses a landmark that is to the east of the balloon and measures the angle of depression to be 54 degrees. A few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is determined to be 61 degrees. Find the height of the balloon.

Answer 1

Answer: Height of the balloon is 588.23 feet.

Explanation:

Since we we have given that

Angle of depression at the landmark to the east of the balloon = 54°

Angle of depression at the landmark to the east of the balloon after travelling 100 feet = 61°

Distance = 100 feet

As we know the formula:

`H=(d)/(\cot x-\cot y)\\\\H=(100)/(\cot 54^\circ-\cot 61^\circ)\\\\H=(100)/(0.72-0.55)\\\\H=(100)/(0.17)\\\\H=588.23\ feet`

Hence, Height of the balloon is 588.23 feet.

Answer 2

The solution would be like this for this specific problem:

sin 54 degrees = Height/718.0624

Height = (sin 54 degrees)(718.0624) = 580.9 ft

So the height of the balloon is 580.9 ft. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.