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

 

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.

Answer 2

Answer: Height of the balloon is 588.23 feet.

Step-by-step 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:

$H=\dfrac{d}{\cot x-\cot y}\\\\H=\dfrac{100}{\cot 54^\circ-\cot 61^\circ}\\\\H=\dfrac{100}{0.72-0.55}\\\\H=\dfrac{100}{0.17}\\\\H=588.23\ feet$

Hence, Height of the balloon is 588.23 feet.