Calculating Horizontal Distance Between Two Hot Air Balloons | Vectors Problem"

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To calculate the horizontal distance between two hot air balloons at heights of 48.8 meters and 52.2 meters, one balloon observer notes the other is at a 13.3-degree angle above the horizontal. The challenge lies in visualizing the problem and correctly positioning the angle within a right triangle formed by the heights and the horizontal distance. A diagram can aid in understanding how to set up the triangle for calculation. Once the triangle is established, trigonometric functions can be applied to find the horizontal distance. Clear visualization and proper use of trigonometry are essential for solving this problem.
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Homework Statement



two hot air balloons are 48.8 and 52.2 meters above the ground. a person in the left balloon observes that the right balloon is 13.3 deg above the horizontal. what is the horizontal distance between the two balloons?

Homework Equations





The Attempt at a Solution


im stuck on how to draw the picture and where to put the 13.3 degrees. if you could attach something of what it is supposed to look like that would be helpful. i can figure out how to make a triangle
 
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[PLAIN]http://img530.imageshack.us/img530/4264/balloon.jpg
 
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Thank you! I understand.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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